Exhibit 10.1

EXECUTION VERSION

SHARE REPURCHASE AGREEMENT

This SHARE REPURCHASE AGREEMENT (this “Agreement”) is entered into as of September 10, 2013 by and between Armstrong World Industries, Inc., a Pennsylvania corporation (the “Company”) and Deutsche Bank Securities Inc. (the “Underwriter”) party to the Underwriting Agreement (as defined below).

Background

A. Pursuant to an underwriting agreement dated the date hereof (the “Underwriting Agreement”) among the Company, The Armstrong World Industries, Inc. Asbestos Personal Injury Settlement Trust, a Delaware trust and a shareholder of the Company (the “Trust”), and Armor TPG Holdings, L.P., a Delaware limited partnership and a shareholder of the Company (together with the Trust, the “Selling Shareholders”) and the Underwriter, the Underwriter will agree to purchase 12,057,382 (the “Underwritten Shares”) of the Company’s common shares, par value $0.01 per share (“Common Shares”) from the Selling Shareholders for sale in an underwritten public offering (the “Public Offering”).

B. The Underwriter has agreed to sell 5,057,382 of the Underwritten Shares (the “Repurchase Shares”) to the Company, and the Company has agreed to purchase the Repurchase Shares from the Underwriter, at the price and upon the terms and conditions set forth in this Agreement (the “Repurchase”).

C. The Company intends to use cash on its balance sheet together with available borrowings under its revolving credit facility and its accounts receivable securitization facility to complete the Repurchase.

D. The board of directors of the Company (the “Board”) established a special committee of the Board (the “Special Committee”) comprised solely of directors of the Company who are not affiliated with the Selling Shareholders and who have no personal financial interest in the Repurchase (each, a “Disinterested Director”) for the purposes of assessing the advisability of the Repurchase, including, without limitation, the timing and amount thereof, and making a recommendation to the Board with respect to such Repurchase.

E. The Special Committee has recommended to the Board that the Board approve the Repurchase and the Board, comprised solely of Disinterested Directors for purposes of approving the Repurchase, has reviewed and approved the Repurchase.

NOW, THEREFORE, in consideration of the mutual covenants herein and other good and valuable consideration, the receipt and sufficiency of which are hereby acknowledged, the undersigned hereby agree as follows:

Agreement

1. Repurchase.

(a) Subject to the satisfaction of the conditions and to the terms set forth in paragraph 1(b) below, the Company hereby agrees to purchase from the Underwriter, and the Underwriter hereby agrees to sell to the Company, at a per share purchase price for each Repurchase Share equal to the per share price at which the Underwriter purchases the Underwritten Shares from the Selling Shareholders in the Public Offering (the “Per Share Purchase Price”), the Repurchase Shares.

(b) (i) The obligations of the Company and the Underwriter to consummate the transactions contemplated by this Agreement shall be subject to (A) the execution of the Underwriting Agreement by the parties thereto, and (B) the closing of the Public Offering pursuant to the terms of the Underwriting Agreement no later than 10 business days after the date hereof; and (ii) the obligations of the Company to consummate the transactions contemplated by this Agreement shall be subject to the receipt by the Special Committee of a fairness opinion from Houlihan Lokey Financial Advisors, Inc. contemporaneously with the execution of the Underwriting Agreement, stating to the effect that the consideration to be paid by the Company to the Underwriter for the Repurchase Shares pursuant to this Agreement is fair to the Company from a financial point of view; the parties hereto hereby acknowledging that, simultaneously with the execution of this Agreement, the Underwriting Agreement has been executed by the parties thereto and the required fairness opinion has been received by the Special Committee and, accordingly, the conditions in paragraph 1(b)(i)(A) and 1(b)(ii) have been satisfied.

(c) The closing of the Repurchase (the “Closing”) shall take place simultaneously with the closing of the Public Offering at the offices of Fried, Frank, Harris, Shriver & Jacobson LLP at One New York Plaza, New York, NY 10004, or at such other time and place as may be agreed upon by the Company and the Underwriter. Payment for the Repurchase Shares shall be made by wire transfer of immediately available funds to the account specified by the Underwriter in an amount equal to the Per Share Purchase Price multiplied by the number of Repurchase Shares being sold to the Company, with any transfer taxes payable in connection with the sale of such Repurchase Shares duly paid by the Company. Payment for the Repurchase Shares shall be made against delivery to the Company of the Repurchase Shares through the facilities of The Depository Trust Company (“DTC”), or as may be agreed upon by the Company and the Underwriter.

2. Company Representations. In connection with the transactions contemplated hereby, the Company represents and warrants to the Underwriter that:

(a) The Company is a corporation duly incorporated and presently subsisting under the laws of the Commonwealth of Pennsylvania. The Company has the requisite corporate power and authority to execute, deliver and perform its obligations under this Agreement and to consummate the transactions contemplated hereby.

(b) This Agreement has been duly authorized, executed and delivered by the Company and constitutes a valid and binding agreement of the Company enforceable in accordance with its terms, except to the extent that enforcement thereof may be limited by bankruptcy, insolvency, reorganization or other laws affecting enforcement of creditors’ rights or by general equitable principles.

2

(c) The compliance by the Company with this Agreement and the consummation of the transactions herein contemplated will not conflict with, result in a breach or violation or imposition of any lien, charge or encumbrance upon any property or assets of the Company or its subsidiaries or constitute a default under (i) the terms of any indenture, contract, lease, mortgage, deed of trust, note agreement, loan agreement or other agreement, obligation, condition, covenant or instrument to which the Company or any of its subsidiaries is a party or by which the Company or any of its subsidiaries is bound or to which any of the property or assets of the Company or any of its subsidiaries is subject, (ii) any provision of the Amended and Restated Articles of Incorporation or Bylaws of the Company or organizational documents of the Company’s subsidiaries or (iii) any statute, law, order, rule, regulation, judgment or decree of any court, regulatory body, administrative agency or governmental agency or body, arbitrator or other authority having jurisdiction over the Company or any of its subsidiaries or any of their properties; except, in the case of clauses (i) and (iii), as would not impair in any material respect the consummation of the Company’s obligations hereunder or reasonably be expected to have a material adverse effect on the financial position, shareholders’ equity or results of operations of the Company and its subsidiaries, taken as a whole, in the case of each such clause, after giving effect to any consents, approvals, authorizations, orders, registrations, qualifications, waivers and amendments as will have been obtained or made as of the date of this Agreement; and no consent, approval, authorization, order, registration or qualification of or with any such court or governmental agency or body is required for the execution, delivery and performance by the Company of its obligations under this Agreement, including the consummation by the Company of the transactions contemplated by this Agreement.

3. Termination. This Agreement shall automatically terminate and be of no further force and effect, in the event that (a) the commencement of the Public Offering has not been publicly announced within three business days after the date hereof or (b) the conditions in paragraph 1(b) of this Agreement have not been satisfied within 10 business days after the date hereof.

4. Notices. All notices, demands or other communications to be given or delivered under or by reason of the provisions of this Agreement will be in writing and will be deemed to have been given when delivered personally, mailed by certified or registered mail, return receipt requested and postage prepaid, or sent via a nationally recognized overnight courier, or sent via email (receipt of which is confirmed) to the recipient. Such notices, demands and other communications will be sent to the addresses indicated below:

To the Company:

Armstrong World Industries, Inc.

2500 Columbia Avenue

P.O. Box 3001

Lancaster, Pennsylvania

Attention: Mark A. Hershey

E-mail Address: MAHershey@armstrong.com

3

With a copy to (which shall not constitute notice):

Morgan, Lewis & Bockius LLP

1701 Market Street

Philadelphia, Pennsylvania 19103

Attention: James W. McKenzie, Jr.

E-mail Address: jmckenzie@morganlewis.com

To the Underwriter:

Deutsche Bank Securities Inc.

60 Wall Street

New York, New York 10005

Attention: ECM Syndicate Desk

Facsimile: (212) 797-9344

With a copy to (which shall not constitute notice):

Fried, Frank, Harris, Shriver & Jacobson LLP

One New York Plaza

New York, New York 10004

Attention: Daniel J. Bursky

E-mail: Daniel.Bursky@friedfrank.com

or such other address or to the attention of such other person as the recipient party shall have specified by prior written notice to the sending party.

5. Miscellaneous.

(a) Survival of Representations and Warranties. All representations and warranties contained herein or made in writing by any party in connection herewith shall survive the execution and delivery of this Agreement and the consummation of the transactions contemplated hereby for a period of eighteen (18) months.

(b) Severability. Whenever possible, each provision of this Agreement will be interpreted in such manner as to be effective and valid under applicable law, but if any provision of this Agreement is held to be invalid, illegal or unenforceable in any respect under any applicable law or rule in any jurisdiction, such invalidity, illegality or unenforceability will not affect any other provision or any other jurisdiction, but this Agreement will be reformed, construed and enforced in such jurisdiction as if such invalid, illegal or unenforceable provision had never been contained herein.

(c) Complete Agreement. This Agreement and any other agreements ancillary thereto and executed and delivered on the date hereof embody the complete agreement and understanding between the parties and supersede and preempt any prior understandings, agreements, or representations by or among the parties, written or oral, which may have related to the subject matter hereof in any way.

4

(d) Counterparts. This Agreement may be executed in separate counterparts, each of which is deemed to be an original and all of which taken together constitute one and the same agreement.

(e) Assignment; Successors and Assigns. Neither this Agreement nor any of the rights, interests or obligations hereunder shall be assigned, in whole or in part, by any of the parties without the prior written consent of the other parties. Subject to the preceding sentence, this Agreement shall bind and inure to the benefit of and be enforceable by the Underwriter and the Company and their respective successors and permitted assigns. Any purported assignment not permitted under this paragraph shall be null and void.

(f) No Third Party Beneficiaries or Other Rights. This Agreement is for the sole benefit of the parties and their successors and permitted assigns and nothing herein express or implied shall give or shall be construed to confer any legal or equitable rights or remedies to any person other than the parties to this Agreement and such successors and permitted assigns.

(g) Governing Law; Jurisdiction. The Agreement and all disputes arising out of or related to this Agreement (whether in contract, tort or otherwise) will be governed by and construed in accordance with the laws of the State of New York. EACH OF THE PARTIES TO THIS AGREEMENT IRREVOCABLY WAIVES ANY AND ALL RIGHTS TO TRIAL BY JURY IN ANY LEGAL PROCEEDING ARISING OUT OF OR RELATED TO THIS AGREEMENT. Each of the parties (i) irrevocably submits to the personal jurisdiction of any state or federal court sitting in Manhattan, as well as to the jurisdiction of all courts to which an appeal may be taken from such courts, in any suit, action or proceeding relating to or arising out of, under or in connection with this Agreement, (ii) agrees that all claims in respect of such suit, action or proceeding, whether arising under contract, tort or otherwise, shall be brought, heard and determined exclusively in such courts, (iii) agrees that it shall not attempt to deny or defeat such personal jurisdiction by motion or other request for leave from such court, and (iv) agrees not to bring any action or proceeding relating to or arising out of, under or in connection with this Agreement or the Company’s business or affairs in any other court, tribunal, forum or proceeding. Each of the parties waives any defense of inconvenient forum to the maintenance of any action or proceeding brought in accordance with this paragraph. Each of the parties agrees that service of any process, summons, notice or document by U.S. registered mail to its address set forth herein shall be effective service of process for any action, suit or proceeding brought against it in accordance with this paragraph, provided that nothing in the foregoing sentence shall affect the right of any party to serve legal process in any other manner permitted by law.

(h) Mutuality of Drafting. The parties have participated jointly in the negotiation and drafting of this Agreement. In the event an ambiguity or question of intent or interpretation arises, this Agreement shall be construed as jointly drafted by the parties, and no presumption or burden of proof shall arise favoring or disfavoring any party by virtue of the authorship of any provision of the Agreement.

(i) Remedies. The parties hereto agree and acknowledge that money damages will not be an adequate remedy for any breach of the provisions of this Agreement, that any breach of the provisions of this Agreement shall cause the other parties irreparable harm, and

5

that any party may in its sole discretion apply to any court of law or equity of competent jurisdiction (without posting any bond or deposit) for specific performance or other injunctive relief in order to enforce, or prevent any violations of, the provisions of this Agreement.

(j) Amendment and Waiver. The provisions of this Agreement may be amended, modified or waived only with the prior written consent of the Underwriter and the Company. No waiver of any of the provisions of this Agreement shall be deemed or shall constitute a waiver of any other provisions of this Agreement, nor shall any waiver constitute a continuing waiver. No failure by any party to insist upon strict performance of any of the provisions of this Agreement or to exercise any right or remedy arising out of a breach thereof shall constitute a waiver of any other provisions or any other breaches of this Agreement.

(k) Further Assurances. Each of the Company and the Underwriter shall execute and deliver such additional documents and instruments and shall take such further action as may be necessary or appropriate to effectuate fully the provisions of this Agreement.

(l) Expenses. Each of the Company and the Underwriter shall bear its own respective expenses in connection with the drafting, negotiation, execution and delivery of this Agreement and the consummation of the transactions contemplated hereby.

(m) Interpretation. The definitions in this Agreement are applicable to the singular as well as the plural forms of such terms.

(n) No Underwriting Commitment. Notwithstanding the foregoing, under no circumstances shall this Agreement be construed to be a commitment by the Underwriter to execute the Underwriting Agreement or underwrite the Underwritten Shares.

[Signatures appear on following page.]

6

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

[Signature Page to Share Repurchase Agreement]

[Signature Page to Share Repurchase Agreement]