Exhibit 10.2

KIRBY CORPORATION

Nonemployee Director Compensation Program

Annual Director Fee

1. Each director will receive an annual fee of $24,000, payable in four equal quarterly payments to be made at the end of each calendar quarter, unless the director elects to receive (a) a stock option for shares of Kirby common stock or (b) restricted shares of Kirby common stock, in lieu of all or part of the cash fee. The fee will be prorated for any director elected between annual stockholder meetings.

2. The election to receive a stock option or restricted stock in lieu of director fees will be made annually. Except as provided in the next sentence, any director who elects to receive a stock option or restricted stock in lieu of all or part of the annual fee for the year following any annual meeting of stockholders must give written notice of that election to Kirby no later than the December 31 preceding such annual meeting. A newly elected director must give written notice of his or her election to receive a stock option or restricted stock in lieu of all or part of the annual fee no later than 30 days after the date of his or her first election as a director.

3. The stock option shall be issued on the following terms:

(a) The number of shares of stock subject to the option will be equal to (i) the portion of the annual fee that a director elects to receive in the form of a stock option divided by (ii) the fair market value of a share of stock on the date of grant multiplied by (iii) 3, with the result then rounded to the nearest whole share.

(b) The exercise price per share will be the fair market value on the date of grant. The fair market value of a share of stock means the closing price on the New York Stock Exchange on the date of reference.

(c) The option will vest one-fourth on the first quarterly payment date, one-fourth on the second quarterly payment date, one-fourth on the third quarterly payment date and one-fourth on the fourth quarterly payment date or, in the case of a director elected between annual stockholder meetings, in equal parts on the remaining quarterly payment dates prior to the first anniversary of the most recent annual meeting of stockholders.

(d) The option will be subject to the terms of the plan under which it is issued, including without limitation provisions relating to vesting, exercise, termination and transferability.

4. The restricted stock shall be issued on the following terms:

(a) The number of shares of restricted stock will be equal to (i) the portion of the annual fee that a director elects to receive in the form of restricted stock divided by (ii) the fair market value of a share of stock on the date of grant multiplied by (iii) 1.2, with the result then rounded to the nearest whole share.

(b) The fair market value of a share of stock means the closing price on the New York Stock Exchange on the date of reference.

(c) The restricted stock will vest one-fourth on the first quarterly payment date, one-fourth on the second quarterly payment date, one-fourth on the third quarterly payment date and one-fourth on the fourth quarterly payment date or, in the case of a director elected between annual stockholder meetings, in equal parts on the remaining quarterly payment dates prior to the first anniversary of the most recent annual meeting of stockholders.

(d) The restricted stock will be subject to the terms of the plan under which it is issued, including without limitation provisions relating to vesting and transferability.

5. Except as provided in the next sentence, the date of grant of an option or restricted stock granted in lieu of the annual fee means the date of the next annual meeting of stockholders after the election by the director to receive a stock option or restricted stock in lieu of cash fees. For a newly elected director, the date of grant means the date of his or her election to receive a stock option or restricted stock in lieu of cash fees.

6. The quarterly payment of cash fees and vesting of stock options and restricted stock are contingent on a director’s continuing to serve in that capacity on each such quarterly payment or vesting date.

Annual Committee Chairman and Presiding Director Fees

1. The Chairman of the Audit Committee will receive an annual fee of $15,000. The Chairmen of the Compensation Committee and the Governance Committee will each receive an annual fee of $10,000. The director selected to be the presiding director at executive sessions of non-management directors will receive an annual fee of $5,000. All of such fees will be payable in four equal quarterly payments to be made at the end of each calendar quarter. The committee chairman and presiding director fees will be prorated for any director who is elected to such position between annual meetings of the board of directors.

2. The quarterly payment of the committee chairman and presiding director fees is contingent on a director’s continuing to serve in such position on each such quarterly payment date.

Meeting Fees

1. Each director will receive a fee of $1,250 for each board meeting attended in person or by telephone.

2. Each member of a committee of the board will receive a fee of $3,000 for each committee meeting attended in person or by telephone.

Automatic Stock Option Grants

1. Each director will receive an option for 10,000 shares of Kirby common stock upon his or her first election as a director.

2. Each director will receive an option for 6,000 shares of Kirby common stock immediately after each annual meeting of stockholders.

3. The exercise price per share in both cases will be the fair market value on the date of grant. The options will be subject to the terms of the plan under which they are issued, including without limitation provisions relating to vesting, exercise, termination and transferability.

Automatic Restricted Stock Grants

1. Each director will receive 1,000 restricted shares of Kirby common stock immediately after each annual meeting of stockholders.

2. The restricted stock will be subject to the terms of the plan under which it is issued, including without limitation provisions relating to vesting and transferability.

Discretionary Stock Option and Restricted Stock Grants

1. The Compensation Committee or the Board of Directors, as applicable, may, in its discretion, grant options and restricted stock to directors as permitted by and subject to the terms of the plan under which such grants are issued, including without limitation provisions relating to vesting, exercise, termination and transferability.

General

1. This compensation program may be amended, modified or terminated by the board at any time.

2. This compensation program applies only to directors of Kirby who are not employees of Kirby or any of its subsidiaries.

3. This compensation program is effective May 27, 2011 and amends and restates in its entirety the Nonemployee Director Compensation Program previously in effect.