Exhibit 10.2

DUNE ENERGY, INC.

2012 STOCK INCENTIVE PLAN

NON-QUALIFIED STOCK OPTION AWARD AGREEMENT

(Non-Employee Directors)

1. Agreement to Grant Option. Subject to the provisions and conditions described in this agreement (the “Agreement”) and the Dune Energy, Inc. 2012 Stock Incentive Plan (as amended and in effect from time to time, the “Plan”), Dune Energy, Inc., a Delaware corporation (the “Company”), hereby agrees to grant to                      (“Participant”) a non-qualified stock option (the “Option”) to acquire from the Company              shares of Common Stock (the “Option Shares”) at the per share exercise price of $         (the “Per Share Exercise Price”), which shall equal to the FMV Per Share on the Grant Date (as defined below) subject to adjustment as provided under the Plan. By execution of this Agreement, Participant agrees to be bound by all of the terms, provisions, conditions and limitations of the Plan as implemented by this Agreement, together with all rules and determinations from time to time issued by the Committee pursuant to the Plan. All capitalized terms not otherwise defined herein shall have the meanings set forth in the Plan, the terms of which are incorporated herein by reference. The Participant hereby acknowledges receipt of a true copy of the Plan and that the Participant has read the Plan carefully and fully understands its content. In the event of any conflict between the terms of this Agreement and the terms of the Plan, the terms of the Plan shall control. No part of the Option granted hereby is intended to qualify as an “incentive stock option” under Section 422 of the Code.

The Participant agrees and understands that nothing contained in this Agreement provides, or is intended to provide, the Participant with any protection against potential future dilution of the Participant’s interest in the Company for any reason, except as otherwise provided by the Plan. The Participant shall have no rights as a stockholder with respect to any shares of Common Stock covered by this Option unless and until the Participant has become the holder of record of the shares, and no adjustments shall be made for dividends in cash or other property, distributions or other rights in respect of any such shares, except as otherwise specifically provided for in the Plan or this Agreement.

2. Grant Date. The grant of such Option shall be effective as of             , 20     (the “Grant Date”).

3. Transferability. Except as provided below, no Option granted hereunder shall be transferable other than by (i) will or by the laws of descent and distribution or (ii) pursuant to a domestic relations order and, during the lifetime of the Participant to whom any such Option is granted, and it shall be exercisable only by the Participant (or his guardian). Any attempt to transfer, assign, pledge, hypothecate or otherwise dispose of, or to subject to execution, attachment or similar process, any Option granted hereunder, or any right thereunder, contrary to the provisions hereof, shall be void and ineffective and shall give no right to the purported transferee. With Committee approval, the Participant (or his guardian) may transfer, for estate planning purposes, all or part of an Option to one or more immediate family members or related family trusts or partnerships or similar entities.

4. Vesting and Exercise.

(a) Vesting. The Option subject to this grant shall become vested as to                  shares of Common Stock on the Grant Date,                  shares of Common Stock on [date of first anniversary of Grant Date], and                  shares of Common Stock on [date of second anniversary of Grant Date], provided the Participant is then a director of the Company. There shall be no proportionate or partial vesting in the periods prior to each vesting date and all vesting shall occur only on the appropriate vesting date, subject to the Participant’s continued service with the Company on each applicable vesting date.

(b) Accelerated Vesting. Notwithstanding the terms of the Plan and Section 4(a) hereof, any unvested portion of this Option shall immediately become vested upon (i) the involuntary removal, by the shareholders of the Company, of the Participant from the Board of Directors of the Company (except for Cause) within one (1) year after the effective date of a Change in Control, or (ii) subject to Board approval, at such times as the Committee, in its discretion, determines. For purposes of this Agreement, “Change in Control” shall be deemed to have occurred upon any of the following events:

(i) the date that any one person, or more than one person acting as a group, acquires ownership of stock of the Company that, together with stock held by such person or group, constitutes more than 50 percent of the total fair market value or total voting power of the stock of the Company;

(ii) The date of any one person, or more than one person acting as a group, acquires (or has acquired during the 12-month period ending on the date of the most recent acquisition by such person or persons) ownership of stock of the Company possessing 35% or more of the total voting power of the stock of the Company;

(iii) The date a majority of members of the Company’s board of directors is replaced during any 12-month period by directors whose appointment or election is not endorsed by a majority of the members of the Company’s board of directors before the date of the appointment or election; or

(iv) the date that any one person, or more than one person acting as a group, acquires (or has acquired during the 12-month period ending on the date of the most recent acquisition by such person or persons) assets from the Company that have a total gross fair market value equal to or more than 50 percent of the total gross fair market value of all of the assets of the corporation immediately before such acquisition or acquisitions.

(c) Expiration. Unless earlier terminated in accordance with the terms and provisions of the Plan and/or this Agreement, all portions of this Option (whether vested or not vested) shall expire and shall no longer be exercisable after the expiration of five (5) years from the Grant Date.

5. Termination. Subject to the terms of the Plan and this Agreement, the Option, to the extent vested at the time of the Participant’s Termination, shall remain exercisable as follows:

(a) Termination due to Death or Disability. In the event of the Participant’s Termination by reason of death or Disability, the vested portion of this Option shall remain exercisable until the earlier of (i) one year from the date of such Termination, and (ii) the expiration of the stated term of the Option pursuant to Section 4 hereof.

(b) Termination for any other reason. In the event of the Participant’s Termination, resignation or removal for any reason (except for death, Disability or Cause), the vested portion of this Option shall remain exercisable until the earlier of (i) [three months from the date of such Termination], and (ii) the expiration of the stated term of the Option pursuant to Section 4 hereof.

(c) Treatment of Unvested Option Shares upon Termination. Any portion of this Option that is not vested as of the date of the Participant’s Termination for any reason shall terminate and expire as of the date of such Termination.

6. Method of Exercise and Payment. Subject to Section 8 hereof, to the extent that the Option has become vested and exercisable with respect to a number of shares of Common Stock as provided herein, the Option may thereafter be exercised by the Participant, in whole or in part, at any time or from time to time prior to the expiration of the Option as provided herein and in accordance with Sections 2.3(b) and 2.3(c) of the Plan, including, without limitation, by the delivery of any form of exercise notice as may be required by the Committee and payment in full of the Per Share Exercise Price multiplied by the number of shares of Common Stock underlying the portion of the Option exercised.

7. Entire Agreement; Amendment. This Agreement, together with the Plan, contains the entire agreement between the parties hereto with respect to the subject matter contained herein, and supersedes all prior agreements or prior understandings, whether written or oral, between the parties relating to such subject matter. The Committee shall have the right, in its sole discretion, to modify or amend this Agreement from time to time in accordance with and as provided in the Plan. The Company shall give written notice to the Participant of any such modification or amendment of this Agreement as soon as practicable after the adoption thereof.

8. Notices. Any notice hereunder by the Participant shall be given to the Company in writing and such notice shall be deemed duly given only upon receipt thereof by the Chief Financial Officer of the Company. Any notice hereunder by the Company shall be given to the Participant in writing and such notice shall be deemed duly given only upon receipt thereof at such address as the Participant may have on file with the Company.

9. No Right to Directorship. Any questions as to whether and when there has been a Termination and the cause of such Termination shall be determined in the sole discretion of the Committee. Nothing in this Agreement shall interfere with or limit in any way the right of the Company to terminate the Participant’s directorship at any time, for any reason and with or without Cause.

10. Withholding of Taxes. The Company shall have the power and the right to deduct or withhold, or require the Participant to remit to the Company, an amount sufficient to satisfy any federal, state, local and foreign taxes of any kind (including, but not limited to, the Participant’s Federal Insurance Contributions Act obligations) which the Company, in its sole discretion, deems necessary to be withheld or remitted to comply with the Code and/or any other applicable law, rule or regulation with respect to the Option and, if the Participant fails to do so, the Company may otherwise refuse to issue or transfer any shares of Common Stock otherwise required to be issued pursuant to this Agreement. Any statutorily required withholding obligation with regard to the Participant may be satisfied by reducing the amount of cash or shares of Common Stock otherwise deliverable upon exercise of the Option.

11. Transfer of Personal Data. The Participant authorizes, agrees and unambiguously consents to the transmission by the Company of any personal data information related to the Option awarded under this Agreement for legitimate business purposes (including, without limitation, the administration of the Plan). This authorization and consent is freely given by the Participant.

12. Section 409A. Notwithstanding anything herein or in the Plan to the contrary, the Option is intended to be exempt from the applicable requirements of Section 409A of the Code and shall be limited, construed and interpreted in accordance with such intent.

13. Binding Agreement; Assignment. This Agreement shall inure to the benefit of, be binding upon, and be enforceable by the Company and its successors and assigns. The Participant shall not assign (except as provided by Section 3 hereof) any part of this Agreement without the prior express written consent of the Company.

14. Headings. The titles and headings of the various sections of this Agreement have been inserted for convenience of reference only and shall not be deemed to be a part of this Agreement.

15. Counterparts. This Agreement may be executed in one or more counterparts, each of which shall be deemed to be an original, but all of which shall constitute one and the same instrument.

16. Further Assurances. Each party hereto shall do and perform (or shall cause to be done and performed) all such further acts and shall execute and deliver all such other agreements, certificates, instruments and documents as either party hereto reasonably may request in order to carry out the intent and accomplish the purposes of this Agreement and the Plan and the consummation of the transactions contemplated thereunder.

17. Acquired Rights. The Participant acknowledges and agrees that: (a) the Company may terminate or amend the Plan at any time; (b) the award of the Option made under this Agreement is completely independent of any other award or grant and is made at the sole discretion of the Company; (c) no past grants or awards (including, without limitation, the Option awarded hereunder) give the Participant any right to any grants or awards in the future whatsoever; and (d) any benefits granted under this Agreement are not part of the Participant’s ordinary compensation, and shall not be considered as part of such compensation in the event of severance, redundancy or resignation.

18. Severability. The invalidity or unenforceability of any provisions of this Agreement in any jurisdiction shall not affect the validity, legality or enforceability of the remainder of this Agreement in such jurisdiction or the validity, legality or enforceability of any provision of this Agreement in any other jurisdiction, it being intended that all rights and obligations of the parties hereunder shall be enforceable to the fullest extent permitted by law.

19. Compliance with Laws. The issuance of this Option (and Option Shares upon exercise of this Option) pursuant to this Agreement shall be subject to, and shall comply with, any applicable requirements of any foreign and U.S. federal and state securities laws, rules and regulations (including, without limitation, the provisions of the Securities Act of 1933, as amended, the 1934 Act and in each case any respective rules and regulations promulgated thereunder) and any other law or regulation applicable thereto. The Company shall not be obligated to issue this Option or any of the Option Shares pursuant to this Agreement if any such issuance would violate any such requirements.

20. Governing Law. All questions concerning the construction, validity and interpretation of this Agreement shall be governed by, and construed in accordance with, the laws of the State of Delaware, without regard to the choice of law principles thereof.

[Remainder of Page Intentionally Left Blank]

IN WITNESS WHEREOF, the parties hereto have executed this Agreement as of the date first written above.