Exhibit 10.3

2004 INCENTIVE PLAN OF DRIL-QUIP, INC.

DIRECTOR RESTRICTED STOCK AWARD AGREEMENT

THIS DIRECTOR RESTRICTED STOCK AWARD AGREEMENT (this “Award”) is made as of May 10, 2012 (the “Grant Date”), by and between Dril-Quip, Inc., a Delaware corporation (the “Company”), and                 (the “Grantee”).

W I T N E S S E T H:

WHEREAS, pursuant to the 2004 Incentive Plan of Dril-Quip, Inc., as amended and restated effective May 10, 2012 (the “Plan”), the Compensation Committee (the “Committee”) of the Board of Directors of the Company (the “Board”) has determined that it would be in the interest of the Company and its stockholders to grant restricted shares of Company common stock, par value $0.01 per share (the “Common Stock”), as provided herein, in order to encourage the Grantee to continue to serve as a member of the Board, to encourage the sense of proprietorship of the Grantee in the Company and to stimulate the active interest of the Grantee in the development and financial success of the Company.

NOW THEREFORE, the Company awards the restricted shares of Common Stock (“Restricted Stock”) to the Grantee, subject to the following terms and conditions of this Award:

1. Grant of Restricted Stock. Subject to the terms and conditions contained herein, including, but not limited to, the restrictions in Sections 3 and 4 of this Award, the Company hereby grants to the Grantee an award of 1,600 shares of Restricted Stock under the Plan. Capitalized terms used, but not otherwise defined, herein shall have the meanings set forth in the Plan.

2. Issuance of Restricted Stock. As of the Grant Date, as determined by the Committee, the shares of Restricted Stock will be (i) registered in a book entry account (“Account”) in the name of the Grantee or (ii) evidenced by the issuance of stock certificates, which certificates will be registered in the name of the Grantee and will bear an appropriate legend referring to the terms, conditions, and restrictions applicable to the Restricted Stock, substantially in the following form:

The transferability of this certificate and the shares of Common Stock represented hereby are subject to the terms, conditions and restrictions (including forfeiture) contained in the Director Restricted Stock Award Agreement, effective as of May 10, 2012, between Dril-Quip, Inc. and the registered owner hereof. Copies of such Award Agreement are on file in the offices of Dril-Quip, Inc., 6401 N. Eldridge Parkway, Houston, Texas 77041.

Any certificates issued that evidence the shares of Restricted Stock shall be held in custody by the Company or, if specified by the Committee, by a third party custodian or trustee, until the restrictions on such shares shall have lapsed, and, as a condition of this Award, the Grantee shall deliver a stock power, duly endorsed in blank, relating to the shares of Restricted Stock. The Restricted Stock will constitute issued and outstanding shares of Common Stock for all corporate purposes.

3. Transfer Restrictions. Except as expressly provided herein, the shares of Restricted Stock are non-transferable and may not otherwise be assigned, pledged, hypothecated or otherwise disposed of and shall not be subject to execution, attachment or similar process. Upon any attempt to effect any such disposition, or upon the levy of any such process, the award provided for herein shall immediately become null and void, and the shares of Restricted Stock shall be immediately forfeited to the Company.

4. Restrictions.

(a) Except as provided in Section 4(b) below, the restrictions on the shares of Restricted Stock shall lapse, and the shares shall vest, in the following percentages on the following vesting dates:

provided, however, that the Grantee has continuously served as a member of the Board from the Grant Date through each of the above vesting dates. Any fractional shares shall be rounded-up to the next whole share (not to exceed the total number of shares of Restricted Stock granted under this Award). If the Grantee does not continuously serve as a member of the Board until the vesting dates specified above, then all shares of then outstanding Restricted Stock shall be forfeited immediately after the Grantee ceases to be a member of the Board.

(b) Notwithstanding the limitations set forth in Section 4(a) above, the Restricted Stock shall become fully vested and exercisable and the restrictions shall lapse as of the date of the occurrence of a Change of Control; provided, however, that the Grantee has continuously served as a member of the Board at all time since the Grant Date. For the purposes of this Award, “Change of Control” shall mean (i) there shall have occurred an event required to be reported with respect to the Company in response to Item 6(e) of Schedule 14A of Regulation 14A (or in response to any similar item or any similar schedule or form) promulgated under the Exchange Act, whether or not the Company is then subject to such reporting requirement; (ii) any “person” (as such term is used in Sections 13(d) and 14(d) of the Exchange Act) shall have become the “beneficial owner” (as defined in Rule 13d-3 under the Exchange Act), directly or indirectly, of securities of the Company representing 30% or more of the combined voting power of the Company’s then outstanding voting securities; (iii) the Company is a party to a merger, consolidation, sale of assets or other reorganization, or a proxy contest, as a consequence of which members of the Board in office immediately prior to such transaction or event constitute less than a majority of the Board thereafter; or (iv) during any period of two consecutive years, individuals who at the beginning of such period constituted the Board (including, for this purpose, any new director whose election or nomination for election by the Company’s stockholders was approved by a vote of at least two-thirds of the directors then still in office who were directors at the beginning of such period) cease for any reason to constitute at least a majority of the Board.

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5. Distribution Following Termination of Restrictions. As soon as administratively feasible following the lapse of restrictions on the Restricted Stock in Section 4 of this Award, but no later than 30 days after such vesting occurs, the Company will cause to be removed from the Account the restrictions or, if requested in writing to the Committee, cause to be issued and delivered to the Grantee (in certificate or electronic form) shares of Common Stock equal to the number of shares of Restricted Stock that have vested (and provided that the Restricted Stock has not been forfeited prior to the date such restrictions lapsed).

6. Voting and Dividend Rights. During the period in which the restrictions provided herein are applicable to the Restricted Stock, the Grantee shall have the right to vote the shares of Restricted Stock and to receive any cash dividends paid with respect thereto unless and until forfeiture thereof. Any dividend or distribution payable with respect to shares of Restricted Stock that shall be paid or distributed in shares of Common Stock shall be subject to the same restrictions provided for herein, and the shares so paid or distributed shall be deemed Restricted Stock subject to all terms and conditions herein. Any dividend or distribution (other than cash or Common Stock) payable or distributable on shares of Restricted Stock, unless otherwise determined by the Committee, shall be subject to the terms and conditions of this Award to the same extent and in the same manner as the Restricted Stock is subject; provided that the Committee may make such modifications and additions to the terms and conditions (including restrictions on transfer and the conditions to the timing and degree of lapse of such restrictions) that shall become applicable to such dividend or distribution as the Committee may provide in its absolute discretion.

7. Adjustments. As provided in Section 16 of the Plan, certain adjustments may be made to the Restricted Stock upon the occurrence of events or circumstances described in Section 16 of the Plan. Without limiting the generality of the foregoing, and except as otherwise provided in the Plan, in the event of any merger, consolidation, reorganization, recapitalization, reclassification or other capital or corporate structure change of the Company, the securities or other consideration receivable for or in conversion of or exchange for shares of Restricted Stock shall be subject to the terms and conditions of this Award to the same extent and in the same manner as the Restricted Stock is subject; provided that the Committee may make such modifications and additions to the terms and conditions (including restrictions on transfer and the conditions to the timing and degree of lapse of such restrictions) that shall become applicable to the securities or other consideration so receivable as the Committee may provide in its absolute discretion.

8. Incorporation of Plan Provisions. This Award and the award of Restricted Stock hereunder are made pursuant to the Plan and are subject to all of the terms and provisions of the Plan as if the same were fully set forth herein. In the event that any provision of this Award conflicts with the Plan, the provisions of the Plan shall control. The Grantee acknowledges receipt of a copy of the Plan and agrees that all decisions under and interpretations of the Plan by the Committee shall be final, binding and conclusive upon the Grantee.

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9. No Rights to Continued Service. Nothing contained in this Award shall confer upon the Grantee any right to continued service as a member of the Board, or limit in any way the right of the Board to terminate or modify the terms of the Grantee’s service at any time.

10. Notice. Unless the Company notifies the Grantee in writing of a different procedure, any notice or other communication to the Company with respect to this Award shall be in writing and shall be delivered personally or sent by first class mail, postage prepaid to the following address:

Dril-Quip, Inc.

6401 N. Eldridge Parkway

Houston, Texas 77041

Attn: Corporate Secretary

Any notice or other communication to the Grantee with respect to this Award shall be in writing and shall be delivered personally, or shall be sent by first class mail, postage prepaid, to the Grantee’s address as listed in the records of the Company on the Grant Date, unless the Company has received written notification from the Grantee of a change of address.

11. Miscellaneous.

(a) THIS AWARD SHALL BE GOVERNED BY AND CONSTRUED IN ACCORDANCE WITH THE LAWS OF THE STATE OF DELAWARE WITHOUT GIVING EFFECT TO THE PRINCIPLES OF CONFLICT OF LAWS.

(b) This Award shall be binding upon and inure to the benefit of the Company and its successors and assigns.

(c) The granting of this Award shall not give the Grantee any rights to similar grants in future years.

(d) If any term or provision of this Award should be invalid or unenforceable, such provision shall be severed from this Award, and all other terms and provisions hereof shall remain in full force and effect.

(e) This Award, including the relevant provisions of the Plan, constitutes the entire agreement between the parties with respect to the subject matter hereof and supersedes all prior agreements and understandings, both written and oral, with respect to the subject hereof. This Award may not be amended, except by an instrument in writing signed by the Company and the Grantee.

(f) This Award may be executed in one or more counterparts, each of which shall be an original, but all of which together shall constitute one and the same instrument.

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