Exhibit 10.1

MARTIN RESOURCE MANAGEMENT CORPORATION

PURCHASE PLAN FOR COMMON UNITS

OF

MARTIN MIDSTREAM PARTNERS, L.P.

(Amended and Restated Effective April 1, 2015)

1. Purpose

Effective July 1, 2006, Martin Resource Management Corporation (the “Company”) adopted the Martin Resource Management Corporation Purchase Plan for Common Units of Martin Midstream Partners L.P. (the “Plan”) to promote the interests of Martin Midstream Partners L.P., a Delaware limited partnership (the “Partnership”) and the Company by providing to employees of the Company and its Affiliates who perform services for the Partnership, where permitted by applicable laws and regulations, the opportunity to acquire an equity interest in the Partnership through the purchase of common units of the Partnership (“Units”). This Plan is not intended to constitute an “employee stock purchase plan” within the meaning of Section 423 of the Internal Revenue Code of 1986, as amended.

Effective April 1, 2015 (the “Restatement Effective Date”), the Plan is hereby amended and restated as set forth in this document.

2. Administration of the Plan

The Plan shall be administered and interpreted by a plan administration committee (the “Committee”) appointed by the Board of Directors of the Company (the “Board”), which Committee shall consist of at least two persons. The Committee shall supervise the administration and enforcement of the Plan according to its terms and provisions and shall have all powers necessary to accomplish these purposes and discharge its duties hereunder including, but not by way of limitation, the power to (i) employ and compensate agents of the Committee for the purpose of administering the accounts of participating employees; (ii) construe and interpret the Plan; (iii) determine all questions of eligibility; and (iv) compute the amount and determine the manner and time of payment of all benefits according to the Plan.

The Committee may act by decision of a majority of its members at a regular or special meeting of the Committee or by decision reduced to writing and signed by all members of the Committee without holding a formal meeting.

3. Nature and Number of Units

The Units subject to issuance under the terms of the Plan shall be authorized but unissued Units, previously issued Units reacquired and held by the Company or Units purchased on the open market. The aggregate number of Units that may be issued under the Plan, including those issued under the Plan prior to the Restatement Effective Date, shall not exceed 1,000,000. All Units purchased under the Plan, regardless of source, shall be counted against the 1,000,000 Unit limitation.

In the event of any reorganization, split, reverse split, distribution, combination of Units, merger, consolidation, offering of rights or other similar change in the capital structure of the Partnership, the Committee may make such adjustment, if any, as it deems appropriate in the number, kind and purchase price of the Units available for purchase under the Plan and in the maximum number of Units that may be issued under the Plan, subject to the approval of the Board and in accordance with Section 18.

4. Eligibility Requirements

Each “Employee” (as hereinafter defined) who performs services for the benefit of the Partnership, as determined by the Committee, shall be eligible for enrollment in the Plan in accordance with Section 5. Participation in the Plan is voluntary.

“Employee” shall mean any individual employed by the Company or an Affiliate (as hereinafter defined). “Affiliate” shall mean any entity (a) that directly or indirectly, through one or more intermediaries, controls, is controlled by or is under common control with, the entity in question. As used herein, the term “control” means the possession, direct or indirect, of the power to direct or cause the direction of the management and policies of an entity, whether through ownership of voting securities, by contract or otherwise; and (b) which has adopted the Plan with the approval of the Committee.

5. Enrollment

Each eligible Employee of the Company participating in the Plan on the day prior to the Restatement Effective Date shall continue to participate in the Plan on the Restatement Effective Date unless he or she elects to suspend payroll deduction contributions to the Plan prior to such date. Each other Employee of the Company who is or become eligible to participate in the Plan on or after the Restatement Effective Date may enroll or re-enroll in the Plan at any time, subject to such limitations as may be imposed by the Committee from time to time. The date an Employee enrolls or re-enrolls in the Plan (or is deemed to re-enroll in the Plan pursuant to Section 8) is referred to herein as an “Enrollment Date.” In order to enroll, an eligible Employee must complete, sign and submit the appropriate forms to the persons designated, or otherwise satisfy any telephonic or electronic enrollment procedure established, by the Committee. Notwithstanding the foregoing, no eligible Employee who is subject to a “blackout period” under the Policy on the Prevention of Insider Trading and Misuse of Confidential Information of Martin Midstream Partners L.P. may enroll in the Plan during any such blackout period.

6. Method of Payment

Payment for Units is to be made as of the applicable “Purchase Date” (as defined in Section 9) with funds accumulated through payroll deductions on an after-tax basis (with no right of prepayment) over the Plan’s designated purchase period (the “Purchase Period”), with the first such deduction commencing as soon as administratively practicable following the Enrollment Date and after the Employee has satisfied the enrollment requirements of Section 5. Each Purchase Period under the Plan shall be a period of three months beginning on each January 1, April 1, July 1 and October 1 and ending on the following March 31, June 30, October 31 or December 31, respectively. Each participating Employee (hereinafter referred to as a “Participant”) will authorize deductions from his pay for each payroll period during the Purchase Period and such amounts will be deducted in conformity with his employer’s payroll deduction schedule.

Each Participant may elect to make contributions each pay period in amounts not less than one percent of compensation and not more than 15 percent of compensation (or such other percentages as the Committee may establish from time to time). For all purposes of the Plan, compensation shall mean salary or wages plus bonuses, overtime and any commissions paid. The rate of contribution shall be designated by the Participant at the time of enrollment and shall be effective as soon as administratively feasible following the Enrollment Date.

A Participant may elect to increase, decrease or suspend the rate of contribution at any time by giving prior written notice to the person designated by the Committee on the appropriate form, or by such other method or procedure prescribed by the Committee, and such election shall be effective as soon as administratively feasible thereafter. Any Participant who suspends payroll deductions during any Purchase Period can resume payroll deductions during such Purchase Period by completing such re-enrollment procedures as may be established by the Committee.

The amount in a Participant’s account including payroll deductions and cash distributions, net of any transaction fees, will be applied to the purchase of Units on the next Purchase Date.

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7. Crediting of Contributions

Contributions shall be credited to a bookkeeping account maintained for such purpose for each Participant as soon as administratively practicable after payroll withholding. Participant contributions will not be maintained in segregated accounts and will not be credited with interest at any time.

8. Grant of Right to Purchase Units on Enrollment

Enrollment in the Plan by an Employee on an Enrollment Date will constitute the grant by the Company to the Participant of the right to purchase Units under the Plan. Re-enrollment by a Participant in the Plan will constitute a grant by the Company to the Participant of a new opportunity to purchase Units on the Enrollment Date on which such re-enrollment occurs. A Participant will have Units purchased for him on the applicable Purchase Date, and he will deemed to be re-enrolled in the Plan on the first day of the Purchase Period immediately following the Purchase Date on which such purchase has occurred, unless such Participant notifies the person designated by the Committee in the appropriate manner that he elects not to re-enroll or has ceased to be eligible to participate in the Plan.

Each right to purchase Units under the Plan during a Purchase Period shall have the following terms:

(a) the right to purchase Units during a particular Purchase Period shall expire on the completion of the purchase of Units on the Purchase Date;

(b) payment for Units purchased will be made only through payroll withholding in accordance with Sections 6 and 7;

(c) purchase of Units will be accomplished only in accordance with Section 9;

(d) the price per Unit will be determined as provided in Section 9;

(e) the right to purchase Units will in all respects be subject to the terms and conditions of the Plan, as interpreted by the Committee from time to time.

9. Purchase of Units

The right to purchase Units granted by the Company under the Plan is for the term of a Purchase Period. Units shall be purchased on or near the last trading day of each calendar quarter ending in March, June, September and December (the “Purchase Date”).

On the Purchase Date, the Committee shall apply the funds then credited to each Participant’s bookkeeping account to the purchase of Units on a national securities exchange. The cost to the Participant for the Units purchased during a Purchase Period shall be the Fair Market Value of Units on the Purchase Date (the “Purchase Price”). For purposes of the foregoing sentence, “Fair Market Value” shall mean the sales price of a Unit on the applicable national securities exchange at the time such Units are purchased. In the event Units are not publicly traded on the Purchase Date, a determination of Fair Market Value shall be made in good faith by the Committee.

Units purchased on behalf of a Participant shall be held by a Custodian selected by the Committee. Units that are held by the Custodian shall be held in a separate account in the name of the Participant. Each Participant shall be credited with the number of whole and fractional Units acquired for such Participant on the Purchase Date. Except as may be otherwise provided pursuant to a procedure established by the Committee, cash distributions on Units held in a Participant’s account in the Plan will be combined with payroll deductions during the Purchase Period and used to purchase Units on the next Purchase Date.

The Company is authorized to withhold from any other amounts payable to a Participant, or it may require the Participant to pay to the Company, all applicable taxes payable upon purchase of any Units and to take such other action as may be necessary in the opinion of the Company to satisfy its withholding obligations for the payment of such taxes.

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If as of any Purchase Date the Units authorized for purchase under the Plan are exceeded, enrollments shall be reduced proportionately to eliminate the excess. Any funds that cannot be applied to the purchase of Units due to excess enrollment shall be refunded as soon as administratively practicable.

10. Withdrawal and Sale of Units

(a) A Participant may elect to withdraw at any time (without withdrawing from participation in the Plan) Units in his account by giving notice to the person designated by the Committee in the appropriate manner. Upon receipt of such notice from the person designated by the Committee, the Custodian will arrange for the issuance and delivery of such Units held in the Participant’s account as soon as administratively practicable.

(b) Notwithstanding anything in the Plan to the contrary, a Participant may sell Units that are held in his account by giving notice to the person designated by the Committee in the appropriate manner. Upon receipt of such notice from the person designated by the Committee, the Custodian will arrange for the sale of such Participant’s Units. Any sale will be deemed to occur on the last business day of the month in which the Participant provides such notice to the person designated by the Committee, or at such other time as the Committee shall establish. The proceeds of any sale under this subsection 10(b), less any associated commissions, shall be paid to the Participant as soon as practicable after the sale.

11. Termination of Participation

The right to participate in the Plan terminates immediately after the Purchase Date if (i) the Participant has suspended payroll deductions during any Purchase Period and has not re-enrolled in the Plan for the next Purchase Period or (ii) the Participant ceases to be eligible to Participate in the Plan.

12. Unpaid Leave of Absence

Unless the Participant has voluntarily withdrawn his contributions from the Plan, Units will be purchased for his account on the Purchase Date next following commencement of an unpaid leave of absence by such Participant, provided such leave does not constitute a termination of employment. The number of Units to be purchased will be determined by applying to the purchase the amount of the Participant’s contributions made up to the commencement of such unpaid leave of absence. If the Participant’s unpaid leave of absence both commences and terminates during the same Purchase Period and he has resumed eligible employment prior to the Purchase Date related to that Purchase Period, he may also resume payroll deductions immediately, and Units will be purchased for him on such Purchase Date as otherwise provided in Section 9.

13. Designation of Beneficiary

Each Participant may designate one or more beneficiaries in the event of death and may, in his sole discretion, change such designation at any time. Any such designation shall be effective upon receipt by the person designated by the Committee and shall control over any disposition by will or otherwise. In the event there is no beneficiary designation in place or if all of the designated beneficiaries have predeceased the Participant, the Participant’s rights under this Plan shall transfer to his or her heirs by will or the laws of descent and distribution, as applicable.

As of the next Purchase Date following the death of a Participant, amounts credited to his account shall be applied to the purchase of Units as provided in Section 9.

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14. Assignment

Except as provided in Section 13, the rights of a Participant under the Plan will not be assignable or otherwise transferable by the Participant, other than by will or the laws of descent and distribution. No purported assignment or transfer of such rights of a Participant under the Plan, whether voluntary or involuntary, by operation of law or otherwise, shall vest in the purported assignee or transferee any interest or right therein whatsoever, but immediately upon such assignment or transfer, or any attempt to make the same, such rights shall terminate and become of no further effect. If this provision is violated, the Participant’s election to purchase Units shall terminate, and the only obligation of the Company remaining under the Plan will be to pay to the person entitled thereto the amount then credited to the Participant’s account. No Participant may create a lien on any funds, securities, rights or other property held for the account of the Participant under the Plan, except to the extent that there has been a designation of beneficiaries in accordance with the Plan, and except to the extent permitted by will or the laws of descent and distribution if beneficiaries have not been designated. A Participant’s right to purchase Units under the Plan shall be exercisable during the Participant’s lifetime only by him.

15. Costs

All costs and expenses incurred in administering this Plan shall be paid by the Company. Any brokerage fees for the sale or transfer of Units purchased under the Plan shall be paid by the Participant.

16. Reports

At the end of each Purchase Period, the Company shall provide or cause to be provided to each Participant a report of his contributions and the number of Units purchased with the amount credited to the Participant’s account as of the Purchase Date for such Purchase Period.

17. Rights as Unitholders

A Participant will have no rights as a Unitholder under the election to purchase until he becomes a Unitholder as herein provided. A Participant will become a Unitholder with respect to Units for which payment has been completed as provided in Section 9 at the close of business on the last business day of the Purchase Period.

18. Modification and Termination

The Board may amend or terminate the Plan at any time insofar as permitted by law. The Plan shall terminate after all Units authorized under the Plan have been purchased, unless terminated earlier by the Board or unless additional Units are authorized by the Board under the Plan. In the event the Plan is terminated, the Committee may elect to terminate all outstanding rights to purchase Units under the Plan either immediately or upon completion of the purchase of Units on the next Purchase Date, unless the Committee has provided that the right to make all such purchases shall expire on some other designated date occurring prior to the next Purchase Date. If the rights to purchase Units under the Plan are terminated prior to expiration, all funds contributed to the Plan that have not been used to purchase Units shall be returned to the Participants as soon as administratively practicable.

19. Board Approval; Effective Date

This amended and restated Plan was adopted by the Board on May 4, 2015, and shall be effective as of the Restatement Effective Date.

20. Governmental Approvals or Consents

This Plan and any offering or sale made to Employees under it are subject to any governmental approvals or consents that may be or become applicable in connection therewith. Subject to the provisions of Section 18, the Board may make such changes in the Plan and include such terms in any offering under the Plan as may be desirable to comply with the rules or regulations of any governmental authority.

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21. Employment Rights

The Plan shall neither impose any obligation on the Company or an Affiliate to continue the employment of any Participant, nor impose any obligation on any Participant to remain in the employ of the Company or an Affiliate.

22. Governing Law

The Plan and rights to purchase Units that may be granted hereunder shall be governed by and construed and enforced in accordance with the laws of the state of Texas.

23. Use of Gender

The gender of words used in the Plan shall be construed to include whichever may be appropriate under any particular circumstances of the masculine, feminine or neuter genders.

24. Other Provisions

The agreements to purchase Units under the Plan, if any, shall contain such other provisions as the Committee and the Board shall deem advisable, provided that no such provision shall in any way be in conflict with the terms of the Plan.

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