VOTING AGREEMENT

Exhibit 10.4

EXECUTION VERSION

VOTING AGREEMENT

This VOTING AGREEMENT is dated as of April 12, 2011 (this “Agreement”), and is among (a) Graham Packaging Company Inc., a Delaware corporation (“Company”), (b) D. Greg Horrigan, (c) Pay It Forward Foundation, (d) Horrigan 2009 Eleven Year Grantor Retained Annuity Trust, (e) Horrigan 2009 Ten Year Grantor Retained Annuity Trust, (f) Horrigan 2009 Nine Year Grantor Retained Annuity Trust, and (g) Horrigan Family Limited Partnership (each of the parties in clauses (b), (c), (d), (e), (f) and (g), a “Stockholder” and collectively, the “Stockholders”).

RECITALS:

WHEREAS, concurrently with the execution of this Agreement, Silgan Holdings Inc. (“Parent”) and the Company are entering into an Agreement and Plan of Merger, dated as of the date hereof (as amended, supplemented, restated or otherwise modified from time to time, the “Merger Agreement”), pursuant to which, among other things, the Company will merge with and into Parent (the “Merger”) and each outstanding share of the common stock, par value $0.01 per share, of the Company (but excluding shares to be canceled or converted in accordance with the Merger Agreement and any Dissenting Shares) will be converted into the right to receive the Merger Consideration specified therein;

WHEREAS, as of the date hereof, each Stockholder is the record and beneficial owner of the number of shares of common stock, par value $0.01 per share (the “Common Stock”), of Parent set forth opposite such Stockholder’s name on Schedule I hereto (the “Existing Shares” and, collectively, with any shares of Common Stock subsequently acquired, whether pursuant to purchase or otherwise and including any shares of Common Stock that such Stockholder has the right to vote or share in the voting of, the “Covered Shares”); and

WHEREAS, as a condition and inducement to the Company entering into the Merger Agreement, the Company has required that the Stockholders agree, and each Stockholder has agreed, to enter into this Agreement.

NOW THEREFORE, in consideration of the foregoing and the mutual representations, warranties, covenants and agreements herein contained, and intending to be legally bound hereby, the parties hereto agree as follows:

ARTICLE I

DEFINED TERMS

1.1. Defined Terms. Capitalized terms used but not otherwise defined herein shall have the meanings ascribed thereto in the Merger Agreement.

1.2. Other Definitions. For purposes of this Agreement:

(a) “beneficial ownership” by a Person of any securities means ownership, directly or indirectly, through any contract, arrangement, understanding, relationship or

otherwise, where such Person has or shares with another Person (i) voting power which includes the power to vote, or to direct the voting of, such security; and/or (ii) investment power which includes the power to dispose, or to direct the disposition, of such security; and shall otherwise be interpreted in accordance with the term “beneficial ownership” as defined in Rule 13d-3 adopted by the SEC under the Exchange Act; provided that for purposes of determining beneficial ownership, a Person shall be deemed to be the Beneficial Owner of any securities which may be acquired by such Person pursuant to any agreement, arrangement or understanding or upon the exercise of conversion rights, exchange rights, warrants or options, or otherwise (irrespective of whether the right to acquire such securities is exercisable immediately or only after the passage of time, including the passage of time in excess of 60 days, the satisfaction of any conditions, the occurrence of any event or any combination of the foregoing). The terms “beneficially own” and “beneficially owned” shall have a correlative meaning.

(b) “Permitted Transfer” means a Transfer of Covered Shares by a Stockholder to any Affiliate if the transferee of such Covered Shares evidences in a writing reasonably satisfactory to the Company such transferee’s agreement to be bound by and subject to the terms and provisions hereof to the same effect as such transferring Stockholder. Notwithstanding anything in the foregoing to the contrary, each of the Stockholders may from time to time Transfer among and between themselves any of the Covered Shares and each such Transfer shall be deemed a Permitted Transfer (it being understood that any Covered Shares so Transferred shall continue to constitute Covered Shares under this Agreement).

(c) “Person” means an individual, corporation, partnership, limited liability company, joint venture, association, trust, unincorporated organization or other entity or a Governmental Entity.

(d) “Transfer” means, directly or indirectly, to sell, transfer, assign, pledge, hypothecate, encumber or dispose of, or to enter into any contract, option or other arrangement or understanding with respect to the voting of or sale, transfer, assignment, pledge, hypothecation, encumbrance or disposition (it being understood that no Transfer shall be deemed to be made by a Stockholder as a result of transfers of limited partnership interests in such Stockholder).

(e) “Voting Period” means the period from and including the date of this Agreement through and including the date on which the Parent Stockholder Approval is obtained.

ARTICLE II

VOTING

2.1. Agreement to Vote. Each Stockholder hereby agrees that, during the term of this Agreement, at the Parent Stockholders’ Meeting and at any other meeting of the stockholders of Parent, however called, including any adjournment or postponement thereof, the Stockholder shall, in each case to the fullest extent that the Covered Shares are entitled to vote thereon, or in any other circumstance in which the vote, consent or other approval of the stockholders of Parent is sought, (a) appear at each such meeting or otherwise cause the Covered

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Shares beneficially owned by the Stockholder as of the applicable record date to be counted as present thereat for purposes of calculating a quorum; and (b) vote (or cause to be voted), in person or by proxy, all of such Stockholder’s Covered Shares over which such Stockholder has voting power as of the applicable record date:

(i) in favor of the adoption of the Merger Agreement, the amendment to the Parent Certificate and the Parent Share Issuance and any other actions related thereto submitted to a stockholder vote pursuant to the Merger Agreement or in furtherance of the Merger;

(ii) against any action or agreement that would result in a breach of any covenant, representation or warranty or any other obligation or agreement of Parent contained in the Merger Agreement, or of any Stockholder contained in this Agreement; and

(iii) against any other action, agreement or transaction involving Parent that would reasonably be expected to impede, interfere with, delay, postpone, discourage, frustrate the purpose of or adversely affect the Merger or the other transactions contemplated by the Merger Agreement or this Agreement or the performance by Parent of its obligations under the Merger Agreement or by any Stockholder of its obligations under this Agreement.

2.2. No Inconsistent Agreements. Each Stockholder hereby, jointly and severally, represents, covenants and agrees that, except for this Agreement, no Stockholder (a) has entered into, or shall enter into at any time while this Agreement remains in effect, any voting agreement, voting trust or similar arrangement with respect to any Covered Shares, or (b) has granted or shall grant at any time while this Agreement remains in effect, a proxy, consent or power of attorney with respect to any Covered Shares (other than as contemplated by Section 2.1).

ARTICLE III

REPRESENTATIONS AND WARRANTIES

3.1. Representations and Warranties of the Stockholders. Each Stockholder, jointly and severally as to itself and each other Stockholder, hereby represents and warrants to the Company as follows:

(a) Authorization; Validity of Agreement; Necessary Action. The Stockholder has the requisite power and authority to execute and deliver this Agreement, to perform its obligations hereunder and to consummate the transactions contemplated hereby. The execution and delivery by the Stockholder of this Agreement and the performance by it of its obligations hereunder and the consummation by it of the transactions contemplated hereby have been duly and validly authorized by the Stockholder and no other actions or proceedings on the part of the Stockholder or any other Person are necessary to authorize the execution and delivery by it of this Agreement, the performance by it of its obligations hereunder or the consummation by it of the transactions contemplated by this Agreement. This Agreement has been duly

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executed and delivered by the Stockholder and, assuming this Agreement constitutes a valid and binding obligation of the Company, constitutes a legal, valid and binding obligation of the Stockholder, enforceable against it in accordance with its terms, subject to the Bankruptcy and Equity Exception.

(b) Ownership. The Stockholder’s Existing Shares are, and all of the Covered Shares of the Stockholder will be through the last day of the Voting Period except to the extent any such Covered Shares are Transferred after the date hereof pursuant to a Permitted Transfer, owned beneficially and of record by the Stockholder. The Stockholder has good and marketable title to the Stockholder’s Existing Shares, free and clear of any Liens other than those imposed by applicable securities laws. As of the date hereof, the Stockholder’s Existing Shares constitute all of the shares of Common Stock beneficially owned or owned of record by the Stockholder. The Stockholder has, and will have through the last day of the Voting Period, the sole voting power (including the right to control such vote as contemplated herein), sole power of disposition, sole power to issue instructions with respect to the matters set forth in Article II hereof, and sole power to agree to all of the matters set forth in this Agreement, in each case with respect to all of the Stockholder’s Covered Shares.

(c) No Violation. The execution and delivery of this Agreement by the Stockholder does not, and the performance by the Stockholder of its obligations under this Agreement will not, (i) conflict with or violate any law, ordinance or regulation of any Governmental Entity applicable to the Stockholder or by which any of its assets or properties is bound, or (ii) conflict with, result in any breach of or constitute a default (or an event that with notice or lapse of time or both would become a default) under, or give to others any rights of termination, amendment, acceleration or cancellation of, or result in the creation of any Lien on the properties or assets of the Stockholder pursuant to, any Contract to which the Stockholder is a party or by which the Stockholder or any of its assets or properties is bound, except for any of the foregoing as could not reasonably be expected, either individually or in the aggregate, to impair the ability of the Stockholder to perform its obligations hereunder or to consummate the transactions contemplated hereby on a timely basis.

(d) No Consent. The execution and delivery of this Agreement by the Stockholder does not, and the performance by it of its obligations under this Agreement and the consummation by it of the transactions contemplated by this Agreement will not, require the Stockholder to obtain any consent, approval, authorization or permit of any Governmental Entity.

3.2. Representations and Warranties of the Company. The Company hereby represents and warrants to the Stockholders as follows:

(a) Authorization; Validity of Agreement; Necessary Action. The Company has the requisite capacity and authority to execute and deliver this Agreement, to perform its obligations hereunder and to consummate the transactions contemplated hereby. This Agreement has been duly executed and delivered by the Company and, assuming this Agreement constitutes a valid and binding obligation of the other parties hereto, constitutes a legal, valid and binding obligation of the Company, enforceable against it in accordance with its terms, subject to the Bankruptcy and Equity Exception.

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(b) No Violation. The execution and delivery of this Agreement by the Company does not, and the performance by the Company of its obligations under this Agreement will not, (i) conflict with or violate any law, ordinance or regulation of any Governmental Entity applicable to the Company or by which any of its assets or properties is bound, or (ii) conflict with, result in any breach of or constitute a default (or an event that with notice or lapse of time or both would become a default) under, or give to others any rights of termination, amendment, acceleration or cancellation of, or result in the creation of any Lien on the properties or assets of the Company pursuant to, any Contract to which the Company is a party or by which the Company or any of its assets or properties is bound, except for any of the foregoing as could not reasonably be expected, either individually or in the aggregate, to impair the ability of the Company to perform its obligations hereunder or to consummate the transactions contemplated hereby on a timely basis.

(c) No Consent. The execution and delivery of this Agreement by the Company does not, and the performance by it of its obligations under this Agreement and the consummation by it of the transactions contemplated by this Agreement will not, require the Company to obtain any consent, approval, authorization or permit of any Governmental Entity.

ARTICLE IV

OTHER COVENANTS

4.1. Prohibition on Transfers, Other Actions. Each Stockholder hereby agrees not to: (i) during the Voting Period, offer to Transfer, Transfer or consent to Transfer any of the Covered Shares or any voting interest therein, unless such Transfer is a Permitted Transfer; (ii) enter into any agreement, arrangement or understanding with any Person, or take any other action, that violates or conflicts with the Stockholder’s covenants and obligations under this Agreement; or (iii) take any action that would restrict the Stockholder’s legal power, authority and right to comply with and perform its covenants and obligations under this Agreement or make any of its representations or warranties contained in this Agreement untrue or incorrect.

4.2. Stock Dividends, etc. In the event of a stock split, stock dividend or distribution, or any change in the Common Stock by reason of any split-up, reverse stock split, recapitalization, combination, reclassification, exchange of shares or the like, the terms “Existing Shares” and “Covered Shares” shall be deemed to refer to and include such shares as well as all such stock dividends and distributions and any securities into which or for which any or all of such shares may be changed or exchanged or which are received in such transaction.

ARTICLE V

MISCELLANEOUS

5.1. Termination. This Agreement shall remain in effect until the earliest to occur of: (a) the Effective Time; (b) the termination of the Merger Agreement in accordance with its terms; (c) the date on which the Board of Directors of the Company (upon the recommendation of the Special Committee) or the Special Committee makes a Company Adverse Recommendation Change; (d) the making of any change, by amendment, waiver, or other

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modification, by any party, to any provision of the Merger Agreement that adversely affects the Stockholders in any material respect, in each case in this clause (d) without the prior written consent of the Stockholders; and (e) the Outside Date; provided that the provisions of this Article V shall survive any termination of this Agreement.

5.2. No Ownership Interest. Nothing contained in this Agreement shall be deemed to vest in the Company any direct or indirect ownership or incidence of ownership of or with respect to any Covered Shares. All rights, ownership and economic benefits of and relating to the Covered Shares shall remain vested in and belong to the Stockholders and the Company shall have no authority to direct the Stockholders in the voting or disposition of any of the Covered Shares, except as otherwise provided herein.

5.3. Notices. All notices and other communications hereunder shall be in writing and shall be deemed given if delivered personally, telecopied (upon telephonic confirmation of receipt), on the first Business Day following the date of dispatch if delivered by a recognized next day courier service or on the third Business Day following the date of mailing if delivered by registered or certified mail, return receipt requested, post prepaid. All notices hereunder shall be delivered as set forth below, or pursuant to such other instructions as may be designated in writing by the party to receive such notice:

Graham Packaging Company Inc.

2401 Pleasant Valley Road

York, Pennsylvania 17402

Fax: (717)  ###-###-####

Attention: Chief Legal Officer

Simpson Thacher & Bartlett LLP

425 Lexington Avenue

New York, New York 10017-3954

Fax: (212)  ###-###-####

Attention: Wilson S. Neely

D. Greg Horrigan

c/o Silgan Holdings Inc.

4 Landmark Square

Suite 400

Stamford, CT 06901

Fax: (203)  ###-###-####

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Silgan Holdings Inc.

4 Landmark Square

Suite 400

Stamford, CT 06901

Fax: (203)  ###-###-####

Attention: Frank W. Hogan, III

Senior Vice President, General Counsel & Secretary

Bryan Cave LLP

1290 Avenue of the Americas

New York, NY 10104

Fax: (212)  ###-###-####

Attention: Robert J. Rawn

5.4. Interpretation. The words “hereof,” “herein” and “hereunder” and words of similar import when used in this Agreement shall refer to this Agreement as a whole and not to any particular provision of this Agreement, and section references are to this Agreement unless otherwise specified. Whenever the words “include,” “includes” or “including” are used in this Agreement, they shall be deemed to be followed by the words “without limitation.” The meanings given to terms defined herein shall be equally applicable to both the singular and plural forms of such terms. The headings contained in this Agreement are for reference purposes only and shall not affect in any way the meaning or interpretation of this Agreement. This Agreement is the product of negotiation by the parties having the assistance of counsel and other advisers. It is the intention of the parties that this Agreement not be construed more strictly with regard to one party than with regard to the others.

5.5. Counterparts. This Agreement may be executed by facsimile or other image scan transmission and in counterparts, all of which shall be considered one and the same agreement and shall become effective when counterparts have been signed by each of the parties and delivered to the other parties, it being understood that all parties need not sign the same counterpart.

5.6. Entire Agreement. This Agreement and, to the extent referenced herein, the Merger Agreement, together with the several agreements and other documents and instruments referred to herein or therein or annexed hereto or thereto, embody the complete agreement and understanding among the parties hereto with respect to the subject matter hereof and supersede and preempt any prior understandings, agreements or representations by or among the parties, written and oral, that may have related to the subject matter hereof in any way.

5.7. Governing Law; Consent to Jurisdiction; Waiver of Jury Trial.

(a) This Agreement shall be governed by and construed in accordance with the laws of the State of Delaware, regardless of the laws that might otherwise govern under applicable principles of conflicts of laws thereof. In addition, each of the parties hereto (i)

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consents to submit itself, and hereby submits itself, to the personal jurisdiction of the Court of Chancery of the State of Delaware and the courts of the United States of America located in the State of New York in the event any dispute arises out of this Agreement or the transactions contemplated by this Agreement, (ii) agrees that it will not attempt to deny or defeat such personal jurisdiction by motion or other request for leave from any such court, and agrees not to plead or claim any objection to the laying of venue in any such court or that any judicial proceeding in any such court has been brought in an inconvenient forum, and (iii) agrees that it will not bring any action relating to this Agreement or the transactions contemplated by this Agreement in any court other than the Court of Chancery of the State of Delaware or a court of the United States of America located in the State of New York.

(b) Each party hereto hereby waives, to the fullest extent permitted by applicable law, any right it may have to a trial by jury in respect of any suit, action or other proceeding arising out of this Agreement or the transactions contemplated hereby. Each party hereto (i) certifies that no representative, agent or attorney of any other party has represented, expressly or otherwise, that such party would not, in the event of any action, suit or proceeding, seek to enforce the foregoing waiver and (ii) acknowledges that it and the other parties hereto have been induced to enter into this Agreement, by, among other things, the mutual waiver and certifications in this Section 5.7.

5.8. Amendment; Waiver. This Agreement may not be amended except by an instrument in writing signed by the Company and the Stockholders. Each party may waive any right of such party hereunder by an instrument in writing signed by such party and delivered to the Company and the Stockholders.

5.9. Remedies.

(a) In the event that any covenant or agreement in this Agreement is not performed in accordance with its terms, each party hereto agrees that the non-breaching party will have the right to an injunction, temporary restraining order, specific performance or other equitable relief in any court of competent jurisdiction enjoining any such breach and enforcing specifically the terms and provisions hereof. Each party hereto agrees not to oppose the granting of such relief in the event a court determines that such a breach has occurred, and to waive any requirement for the securing or posting of any bond in connection with such remedy. Notwithstanding anything in this Agreement to the contrary, such remedies as provided herein shall be the exclusive remedies of the parties hereto, and each party hereto waives all other remedies, including monetary remedies, with respect to any breaches of the terms hereof.

(b) All rights, powers and remedies provided under this Agreement or otherwise available in respect hereof at law or in equity shall be cumulative and not alternative, and the exercise or beginning of the exercise of any thereof by any party shall not preclude the simultaneous or later exercise of any other such right, power or remedy by such party.

5.10. Severability. Any term or provision of this Agreement which is determined by a court of competent jurisdiction to be invalid or unenforceable in any jurisdiction shall, as to that jurisdiction, be ineffective to the extent of such invalidity or unenforceability without rendering invalid or unenforceable the remaining terms and provisions of this Agreement or affecting the

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validity or enforceability of any of the terms or provisions of this Agreement in any other jurisdiction, and if any provision of this Agreement is determined to be so broad as to be unenforceable, the provision shall be interpreted to be only so broad as is enforceable, in all cases so long as neither the economic nor legal substance of the transactions contemplated hereby is affected in any manner adverse to any party or its stockholders. Upon any such determination, the parties shall negotiate in good faith in an effort to agree upon a suitable and equitable substitute provision to effect the original intent of the parties as closely as possible and to the end that the transactions contemplated hereby shall be fulfilled to the maximum extent possible.

5.11. Successors and Assigns; Third Party Beneficiaries. Except in connection with a Permitted Transfer as provided herein, neither this Agreement nor any of the rights or obligations of any party under this Agreement shall be assigned, in whole or in part, by any party without the prior written consent of the other parties hereto. Subject to the foregoing, this Agreement shall bind and inure to the benefit of and be enforceable by the parties hereto and their respective successors, permitted assigns, heirs and legal representatives. Nothing in this Agreement, express or implied, is intended to confer on any Person other than the parties hereto or their respective successors and permitted assigns, any rights, remedies, obligations or liabilities under or by reason of this Agreement.

5.12. Capacity as a Stockholder. Each Stockholder makes its agreements and understandings herein solely in its capacity as the record holder and beneficial owner of the Covered Shares. Notwithstanding anything to the contrary herein, nothing herein shall limit or affect any actions taken by the Stockholders or their Representatives and Affiliates or any other Person solely in their capacity as directors or officers of Parent, and none of such actions taken shall be deemed to constitute a breach of this Agreement by the Stockholder.

5.13. Joint and Several Liability. The Stockholders hereby agree that all representations, warranties, covenants, agreements, liabilities and obligations under this Agreement are joint and several to the Stockholders, and each Stockholder will be liable to the fullest extent provided for in this Agreement for any breach, default, liability or other obligation of each of the other Stockholders.

5.15. Fees and Expenses. Each party hereto shall pay its own fees and expenses (including those of its counsel and other advisors) incurred in connection with this Agreement.

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IN WITNESS WHEREOF, the parties hereto have caused this Agreement to be signed (where applicable, by their respective officers or other authorized Person thereunto duly authorized) as of the date first written above.

[Signature Page to Voting Agreement]

[Signature Page to Voting Agreement]

Schedule I

STOCKHOLDER INFORMATION