Shaw (SHAW) 10-K/A 2004 FY Annual report (amended)

EXHIBIT 32.1

CERTIFICATION OF CHIEF EXECUTIVE OFFICER OF THE SHAW GROUP INC. PURSUANT TO
18 U.S.C. SECTION 1350,
AS ADOPTED PURSUANT TO
SECTION 906 OF THE SARBANES-OXLEY ACT OF 2002

In connection with the Annual Report of The Shaw Group Inc. (the “Company”) on Form 10-K/A (Amendment 1) for the fiscal year ended August 31, 2004, as filed with the Securities and Exchange Commission on the date hereof (the “Report”), I, J.M. Bernhard, Jr., Chief Executive Officer of the Company, hereby certify, pursuant to 18 U.S.C. Section 1350, as adopted pursuant to Section 906 of the Sarbanes-Oxley Act of 2002, that:

(1)	The Report fully complies with the requirements of section 13(a) or 15(d) of the Securities Exchange Act of 1934; and
(2)	The information contained in the Report fairly presents, in all material respects, the financial condition and results of operations of the Company.

July 11, 2005
	/s/ J. M. Bernhard, Jr. J. M. Bernhard, Jr. Chief Executive Officer