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EXHIBIT 31.1 CERTIFICATION OF CHIEF EXECUTIVE OFFICER OF THE SHAW GROUP INC.
PURSUANT TO 15 U.S.C. SECTION 7241, AS ADOPTED
PURSUANT TO SECTION 302 OF THE SARBANES-OXLEY ACT OF 2002 I, J.M. Bernhard, Jr., Chief Executive Officer of The Shaw Group Inc.,
certify that:  1.
    
    I have reviewed this Annual Report on Form 10-K for the fiscal year ended
August 31, 2004 (the Annual Report) of The Shaw Group Inc.;2.
    
    Based on my knowledge, this Annual Report does not contain any untrue
statement of a material fact or omit to state a material fact necessary to
make the statements made, in light of the circumstances under which such
statements were made, not misleading with respect to the period covered by
this Annual Report;3.
    
    Based on my knowledge, the financial statements and other financial
information included in this Annual Report, fairly present in all material
respects the financial condition, results of operations and cash flows of
the registrant as of, and for, the periods presented in this Annual
Report;4.
    
    The registrants other certifying officer and I are responsible for
establishing and maintaining disclosure controls and procedures (as
defined in Exchange Act Rules 13a-15(e) and 15d-15(e)) for the registrant
and we have:  a.
    
    designed such disclosure controls and procedures, or caused such
disclosure controls and procedures to be designed under our
supervision, to ensure that material information relating to the
registrant, including its consolidated subsidiaries, is made known to
us by others within those entities, particularly during the period in
which this Annual Report is being prepared;b.
    
    evaluated the effectiveness of the registrants disclosure controls
and procedures and presented in this Annual Report our conclusions
about the effectiveness of the disclosure controls and procedures, as
of the end of the period covered by this Annual Report based on such
evaluation; andc.
    
    disclosed in this Annual Report any changes in the registrants
internal control over financial reporting that occurred during the
registrants most recent fiscal quarter (the registrants fourth fiscal
quarter in the case of an Annual Report) that has materially affected,
or is reasonably likely to materially affect, the registrants internal
control over financial reporting; and  5.
    
    The registrants other certifying officer and I have disclosed, based on
our most recent evaluation of internal control over financial reporting,
to the registrants auditors and the audit committee of registrants board
of directors (or persons performing the equivalent functions):  a.
    
    all significant deficiencies and material weaknesses in the design
or operation of internal control over financial reporting which are
reasonably likely to adversely affect the registrants ability to
record, process, summarize and report financial information; andb.
    
    any fraud, whether or not material, that involves management or
other employees who have a significant role in the registrants
internal control over financial reporting. Date: November 2, 2004
    
    /s/ J. M. Bernhard, Jr.
J. M. Bernhard, Jr.
Chief Executive Officer