EXHIBIT B

Lock-Up Agreement dated September 7, 2010

DEUTSCHE BANK SECURITIES, INC.
60 Wall Street, 44th Floor
New York, New York 10005

     Re:      Proposed Offering by DryShips Inc.

Ladies and Gentlemen:

     The undersigned, a stockholder, officer and director of DryShips Inc., a Marshall Islands corporation (the “Company”), understands that Deutsche Bank Securities Inc. (“Deutsche Bank”) proposes to enter into a Sales Agreement (the “Sales Agreement”) with the Company providing for the public offering of shares (the “Securities”) of the Company’s common stock, par value $0.01 per share (the “Common Stock”), pursuant to a Registration Statement on Form F-3. In recognition of the benefit that such an offering will confer upon the undersigned as a stockholder, officer and director of the Company, and for other good and valuable consideration, the receipt and sufficiency of which are hereby acknowledged, the undersigned agrees with Deutsche Bank that, during a period of 90 days from the date of the most recently filed Prospectus Supplement(as defined in the Sales Agreement), the undersigned will not, without the prior written consent of Deutsche Bank, directly or indirectly (i) offer, pledge, sell, contract to sell, sell any option or contract to purchase, purchase any option or contract to sell, grant any option, right or warrant for the sale of, lend or otherwise dispose of or transfer any shares of the Company’s Common Stock or any securities convertible into or exchangeable or exercisable for Common Stock, whether now owned or hereafter acquired by the undersigned or with respect to which the undersigned has or hereafter acquires the power of disposition, or file, or cause to be filed, any registration statement under the Securities Act of 1933, as amended, with respect to any of the foregoing (collectively, the “Lock-Up Securities”) or (ii) enter into any swap or any other agreement or any transaction that transfers, in whole or in part, directly or indirectly, the economic consequence of ownership of the Lock-Up Securities, whether any such swap or transaction is to be settled by delivery of Common Stock or other securities, in cash or otherwise.

     Notwithstanding the foregoing, and subject to the conditions below, the undersigned may transfer the Lock-Up Securities without the prior written consent of Deutsche Bank, provided that (1) Deutsche Bank receives a signed lock-up agreement for the balance of the lockup period from each donee, trustee or transferee, as the case may be, (2) any such transfer shall not involve a disposition for value, (3) such transfers are not required to be reported in any public report or filing with the Securities and Exchange Commission, or otherwise and (4) the undersigned does not otherwise voluntarily effect any public filing or report regarding such transfers:

          (1) as a bona fide gift or gifts; or

          (2) to any trust or other entity for the direct or indirect benefit of, or wholly-owned by, the undersigned or the immediate family of the undersigned (for purposes of this lock-up agreement, “immediate family” shall mean any relationship by blood, marriage or adoption, not more remote than first cousin).

     Notwithstanding the foregoing, if:

     (1) during the last 17 days of the 90-day lock-up period, the Company issues an earnings release or material news or a material event relating to the Company occurs; or

     (2) prior to the expiration of the 90-day lock-up period, the Company announces that it will release earnings results or becomes aware that material news or a material event will occur during the 16-day period beginning on the last day of the 90-day lock-up period,

the restrictions imposed by this lock-up agreement shall continue to apply until the expiration of the 18-day period beginning on the issuance of the earnings release or the occurrence of the material news or material event, as applicable, unless Deutsche Bank waives, in writing, such extension.

     The undersigned hereby acknowledges and agrees that written notice of any extension of the 90-day lock-up period pursuant to the previous paragraph will be delivered by Deutsche Bank to the Company (in accordance with Section 12 of the Sales Agreement) and that any such notice properly delivered will be deemed to have been given to, and received by, the undersigned. The undersigned further agrees that, prior to engaging in any transaction or taking any other action that is subject to the terms of this lock-up agreement during the period from the date of this lock-up agreement to and including the 34th day following the expiration of the initial 90-day lock-up period, it will give notice thereof to the Company and will not consummate such transaction or take any such action unless it has received confirmation from the Company that the 90-day lock-up period (as may have been extended pursuant to the previous paragraph) has expired.

     The undersigned hereby waives, until the expiration of this agreement, any rights of the undersigned to sell any Lock-Up Securities or any other security issued by the Company pursuant to the Registration Statement and acknowledges and agrees that until the expiration of this agreement, the undersigned will not request the Company to register under the Securities Act of 1933 such Lock-Up Securities or other securities beneficially owned by the undersigned.

     The undersigned understands and agrees that the agreements of the undersigned are irrevocable and shall be binding upon the undersigned’s heirs, legal representatives, successors and assigns.

     The undersigned also agrees and consents to the entry of stop transfer instructions with the Company’s transfer agent and registrar against the transfer of the Lock-Up Securities except in compliance with the foregoing restrictions.

     Notwithstanding the foregoing, this agreement shall terminate and be of no further force and effect upon a decision by Deutsche Bank Securities Inc. or the Company not to proceed with the sale of any Securities prior to the first sale of Securities under the Sales Agreement, which decision shall be set forth in writing and delivered to each of the parties hereto and to the Company.

Very truly yours,
Signature:	/s/ George Economou
Print Name:	George Economou