Exhibit 4.1

AMENDMENT TO RIGHTS AGREEMENT

     This Amendment, dated as of December 9, 2010 (this “Amendment”), amends that certain Rights Agreement, dated as of July 9, 2001 (the “Rights Agreement”), between The Shaw Group Inc., a Louisiana corporation (the “Company”), and American Stock Transfer & Trust Company, LLC (successor in interest to Wachovia Bank, a division of Wells Fargo Bank, N.A., in turn successor in interest to First Union National Bank), as rights agent (the “Rights Agent”). Except as otherwise expressly provided herein, or unless the context otherwise requires, all terms used herein have the meanings assigned to them in the Rights Agreement.

     WHEREAS, pursuant to Section 27 of the Rights Agreement, the Board of Directors (the “Board”) of the Company may, and the Rights Agent shall, if so directed, from time to time supplement or amend any provision of the Rights Agreement in accordance with the provisions of Section 27 thereof;

     WHEREAS, the Board has determined that it is in the best interests of the Company and its shareholders to amend the Rights Agreement as set forth herein; and

     WHEREAS, all acts necessary to make this Amendment a valid agreement, enforceable according to its terms, have been done and performed, and the execution and delivery of this Amendment by the Company and the Rights Agent have been in all respects duly authorized by the Board and the Rights Agent.

     NOW, THEREFORE, in consideration of the foregoing and the mutual agreements set forth herein, and intending to be legally bound, the parties hereto agree as follows:

     A. Amendment of Section 7(a). Section 7(a) of the Rights Agreement is hereby amended and supplemented by deleting the clause in Section 7(a) that provides “(i) the Close of Business on July 9, 2011 (the “Final Expiration Date”)” and replacing it with the following: “(i) the Close of Business on December 31, 2010 (the “Final Expiration Date”)”.

     B. Amendment of Exhibits. The Exhibits to the Rights Agreement shall be restated to reflect this Amendment, including all conforming changes.

     C. Effectiveness. This Amendment shall be deemed effective as of the date first written above, as if executed on such date.

     D. Governing Law. This Amendment shall be deemed to be a contract under the laws of the State of Louisiana and for all purposes shall be governed by and construed in accordance with the laws of such state applicable to contracts to be made and performed entirely within such state.

     E. Severability. If any provision, covenant or restriction of this Amendment is held by a court of competent jurisdiction or other authority to be invalid, illegal or unenforceable, the remainder of the terms, provisions, covenants and restrictions of this Amendment shall remain in full force and effect and shall in no way be effected, impaired or invalidated.

     F. Counterparts. This Amendment may be executed in any number of counterparts and each of such counterparts shall for all purposes be deemed to be an original, and all such counterparts together constitute but one and the same original.

     IN WITNESS WHEREOF, the parties hereto have caused this Amendment to be duly executed, as of the date first set forth above.