Exhibit 10.4

DUNE ENERGY, INC.

2012 STOCK INCENTIVE PLAN

RESTRICTED STOCK AGREEMENT

(Employees/Performance Based Agreement)

1. Agreement to Grant Restricted Shares. 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”) all rights, title and interest in the record and beneficial ownership of                      (                ) shares (the “Restricted Shares”) of common stock, $.001 par value per share, of the Company (“Common Stock”). 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.

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

3. Issuance and Transferability. Each certificate representing the shares of Restricted Stock awarded under the Plan shall be registered in the name of the Participant and, during the Restricted Period, shall be left in deposit with the Company and a stock power endorsed in blank until such time as the restrictions on transfer have lapsed. Any certificate or certificates representing Restricted Shares shall bear a legend similar to the following:

“The shares represented by this certificate have been issued pursuant to the terms of the Dune Energy, Inc. 2012 Stock Incentive Plan (as amended and restated) and may not be sold, pledged, transferred, assigned or otherwise encumbered in any manner except as is set forth in the terms of such Plan or award dated             , 20    .”

Until all restrictions lapse, the Restricted Shares shall not be (i) assignable, saleable, or otherwise transferable by the Participant except by will or by the laws of descent and distribution or pursuant to a domestic relations order, or (ii) subject to any encumbrance, pledge or charge of any nature. Notwithstanding the foregoing, in the case of Participant’s death or Disability, Participant’s rights under this Agreement may be exercised by Participant’s legal guardian (if the Participant becomes Disabled) or Participant’s legal representative or beneficiary. The executor or administrator of the Participant’s estate, or the person or persons to whom the Participant’s rights under this Agreement will pass by will or the laws of descent or distribution, shall be deemed to be the Participant’s beneficiary or beneficiaries of the rights of the Participant hereunder and shall be entitled to exercise such rights as are provided hereunder. Any attempted transfer in violation of the Plan or this Agreement shall be void and ineffective for all purposes.

4. Risk of Forfeiture. Participant shall immediately forfeit all rights pursuant to this Agreement and to any nonvested portion of the Restricted Shares in the event of the Participant’s termination of employment from or services to the Company under circumstances that do not cause such restrictions to lapse and the Participant to become fully vested under the terms of this Agreement. The Restricted Shares allocated to a performance period in which the Participant does not vest due to the level of achievement of the TSR Performance goals (as defined below and determined in accordance with this Agreement and the Plan) for such performance period, as determined by the Committee in accordance with the Plan and this Agreement, will be forfeited. In the event the Participant is terminated for Cause, Participant shall forfeit all rights to Restricted Shares (both vested and nonvested portions) at 12:01 a.m. on the date of termination.

5. Repurchase & Recover Rights. The Company shall have the right to repurchase or recover such shares for the amount of cash paid therefor, if any, if (i) the Participant shall terminate Employment from or services to the Company prior to the lapse of such restrictions under circumstances that do not cause such restrictions to lapse and Participant to become fully vested or (ii) the Restricted Shares are forfeited by the Participant pursuant to the terms of the Agreement.

6. Vesting. Subject to Paragraphs 3 & 4 hereof and notwithstanding the terms of the Plan, Participant shall vest in all rights under the Restricted Shares and any rights of the Company to such shares shall lapse with respect to the Restricted Shares on the applicable anniversary of the Grant Date based upon the attainment of TSR Performance goals (as defined below and determined in accordance with this Agreement and the Plan) during the applicable Performance Period provided that the Participant is continuously employed by the Company from the Grant Date to the applicable anniversary of the Grant Date.

For purposes of this Agreement, the following definitions apply:

(a) “Performance Period A” means the period beginning on the first day of the fiscal quarter in which the Grant Date occurs and ending on the last day of the fiscal quarter ending prior to the first anniversary of the Grant Date.

(b) “Performance Period B” means the period beginning on the first day of the fiscal quarter in which the first anniversary of the Grant Date occurs and ending on the last day of the fiscal quarter ending prior to the second anniversary of the Grant Date.

(c) “Performance Period C” means the period beginning on the first day of the fiscal quarter in which the second anniversary of the Grant Date occurs and ending on the last day of the fiscal quarter ending prior to the third anniversary of the Grant Date.

(d) “Peer Group” refers to the following companies:

Notwithstanding the foregoing, (i) if any company included in the Peer Group ceases to be publicly traded by reason of merger, acquisition, liquidation, bankruptcy, or any other reason, the Committee may, in its sole discretion, add a replacement company to the Peer Group, and (ii) for any other reason the Committee deems appropriate, the Committee may, in its sole discretion, make modifications to the Peer Group.

(e) “Total Stock Return” refers to the percentage growth in share price, adjusted for dividends and stock splits, over the applicable Performance Period, as measured by comparing (i) the average share price for the 30-day period, or such other shorter period that the Committee may determine, counting from the first day of the applicable Performance Period to (ii) the average share price for the 30-day period, or such other shorter period that the Committee may determine, ending on the last day of the applicable Performance Period. For example, if the share price, adjusted for dividends and stock splits, increases over the applicable Performance Period from $0.15 to $0.24, Total Stock Return is 60% (($0.24/$0.15) - 1).

(f) “TSR Performance” is the percentile rank of the Company among the Peer Group. In determining TSR Performance, all companies in the Peer Group, as well as the Company, shall be ranked from lowest-to-highest in Total Stock Return. The Company’s percentile rank shall thereafter be computed as follows:

Percentile = [       100 x (Rank of the Company – 0.5)       ]

              (Number of companies in Peer Group + 1)

Vesting shall occur as follows:

Vesting based on TSR Performance. Over Performance Period A, if the Company’s TSR Performance equals or exceeds the 75^th percentile of the Peer Group, 100% of [1/3 of the total Restricted Shares] shares shall vest on [date of first anniversary of the Grant Date]; if the Company’s TSR Performance equals or exceeds the 50^th percentile but falls below the 75^th percentile of the Peer Group, 75% of [1/3 of the total Restricted Shares] shares shall vest on [date of first anniversary of the Grant Date]; and if the Company’s TSR Performance equals or exceeds the 25^th percentile but falls below the 50^th percentile of the Peer Group, 50% of [1/3 of the total Restricted Shares] shares shall vest on [date of first anniversary of the Grant Date].

Over Performance Period B, if the Company’s TSR Performance equals or exceeds the 75^th percentile of the Peer Group, 100% of [1/3 of the total Restricted Shares] shares shall vest on [date of second anniversary of the Grant Date]; if the Company’s TSR Performance equals or exceeds the 50^th percentile but falls below the 75^th percentile of the Peer Group, 75% of [1/3 of the total Restricted Shares] shares shall vest on [date of second anniversary of the Grant Date]; and if the Company’s TSR Performance equals or exceeds the 25^th percentile but falls below the 50^th percentile of the Peer Group, 50% of [1/3 of the total Restricted Shares] shares shall vest on [date of second anniversary of the Grant Date].

Over Performance Period C, if the Company’s TSR Performance equals or exceeds the 75^th percentile of the Peer Group, 100% of [1/3 of the total Restricted Shares] shares shall vest on [date of third anniversary of the Grant Date]; if the Company’s TSR Performance equals or exceeds the 50^th percentile but falls below the 75^th percentile of the Peer Group, 75% of [1/3 of the total Restricted Shares] shares shall vest on [date of third anniversary of the Grant Date]; and if the Company’s TSR Performance equals or exceeds the 25^th percentile but falls below the 50^th percentile of the Peer Group, 50% of [1/3 of the total Restricted Shares] shares shall vest on [date of third anniversary of the Grant Date].

Otherwise, none shall vest.

In addition, subject to Paragraphs 3 & 4 and notwithstanding the terms of the Plan, Participant shall vest in all rights under the Restricted Shares that have not previously been forfeited and any rights of the Company to such shares shall lapse with respect to the Restricted Shares upon (i) termination of the Participant by the Company for any reason (except for Cause) within one (1) year after the effective date of a Change in Control, or (ii) subject to Board approval, at such other times as the Committee, in its discretion, determines.

Upon vesting of the Restricted Shares, the Committee shall issue and deliver to Participant a certificate for such shares without the legend set forth in Section 3 above for the number of shares that are no longer subject to such restrictions, terms and conditions, less the shares withheld for taxes, if, such withholding is permitted pursuant to the Plan and at the sole discretion of the Committee.

7. Ownership Rights/Dividends. Subject to the reservations set forth in this Agreement, the Plan and Paragraph 9, upon Participant’s grant of the Restricted Shares, the Participant shall have all the rights of a stockholder with respect to such shares including the right to vote and the right to receive dividends or other distributions paid or made with respect to such shares. The Restricted Shares shall be registered in the name of the Participant and at the address set forth below the Participant’s signature attached hereto.

8. Reorganization of the Company. The existence of this Agreement shall not affect in any way the right or power of the Company or its stockholders to make or authorize any or all adjustments, recapitalizations, reorganizations or other changes in the Company’s capital structure or its business; any merger or consolidation of the Company; any issue of bonds, debentures, preferred or prior preference stock ahead of or affecting the Restricted Shares or the rights thereof; the dissolution or liquidation of the Company, or any sale or transfer of all or any part of its assets or business, or any other corporate act or proceeding, whether of a similar character or otherwise.

9. Certain Restrictions. By executing this Agreement, Participant acknowledges that he will enter into such written representations, warranties and agreements and execute such documents as the Company may reasonably request in order to comply with the securities law or any other applicable laws, rules or regulations, or with this document or the terms of the Plan.

10. No Guarantee of Employment. The grant of Restricted Shares shall not be construed as giving the Participant the right to be retained in the employ of the Company. Further, the Company may at any time dismiss the Participant from employment, free from any liability or any claim under the Plan or this Agreement, unless otherwise expressly provided in the Plan or this Agreement.

11. Withholding of Taxes. Any issuance of Common Stock pursuant to this Agreement shall not be made until appropriate arrangements satisfactory to the Company have been made for the payment of any tax amounts (federal, state, local or other) that may be required to be withheld or paid to the Company with respect thereto.

12. No Guarantee of Tax Consequences. None of the Board, the Company or the Committee makes any commitment or guarantee that any federal, state or local tax treatment will (or will not) apply or be available to any person eligible for the benefits under this Agreement.

13. No Right to Section 83(b) Election. The Participant shall have no right to file a Code Section 83(b) election in connection with this Agreement.

14. Severability. In the event that any provision of the Agreement shall be held illegal, invalid, or unenforceable for any reason, such provision shall be construed or deemed amended to conform with the applicable laws, or if it cannot be construed or deemed amended without, in the determination of the Committee, materially altering the intent of the Plan or the Agreement, such provision shall be fully severable and shall not affect the remaining provisions of the Agreement, and the Agreement shall be construed and enforced as if the illegal, invalid, or unenforceable provision had never been included herein.

15. Governing Law. This Agreement shall be determined in accordance with applicable federal law and the laws of the State of Delaware, without regard to any principles of conflicts of law.

IN WITNESS WHEREOF, the Agreement is executed this     day of         20    .