UNITED STATES
                       SECURITIES AND EXCHANGE COMMISSION

                             Washington, D.C. 20549

                           ---------------------------

                                    FORM 8-K

                                 CURRENT REPORT

                     Pursuant to Section 13 or 15(d) of the
                         Securities Exchange Act of 1934

                Date of Report (Date of Earliest Event Reported)
                                   May 5, 2004

                               THE SHAW GROUP INC.
             (Exact name of registrant as specified in its charter)

<Table>
<Caption>
          Louisiana                             1-12227                           72-1106167
                                                                  
(State or other jurisdiction of         (Commission File Number)       (IRS Employer Identification No.)
       incorporation)
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                  4171 Essen Lane, Baton Rouge, Louisiana 70809
              (Address of principal executive offices and zip code)

                                 (225) 932-2500
              (Registrant's telephone number, including area code)

                                 Not Applicable
          (Former name or former address, if changed since last report)




ITEM 5.  OTHER EVENTS.

         On May 3, 2004, The Shaw Group Inc. issued a press release that is
filed herewith as Exhibit 99.1.

ITEM 7.  FINANCIAL STATEMENTS AND EXHIBITS.

         (c)      Exhibits:

                  99.1. Press Release dated May 3, 2004 - The Shaw Group Inc.
         Announces Preliminary Results of Tender Offer for its Outstanding
         Liquid Yield Option(TM) Notes.


                                   SIGNATURES

         Pursuant to the requirements of the Securities Exchange Act of 1934,
the registrant has duly caused this report to be signed on its behalf by the
undersigned hereunto duly authorized.

                                    THE SHAW GROUP INC.
                                         (Registrant)

Date:      May 5, 2004              By: /s/ Robert L. Belk
                                        --------------------------------------
                                        Robert L. Belk, Executive Vice President
                                        and Chief Financial Officer


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                               THE SHAW GROUP INC.

                                  EXHIBIT INDEX

                                    Form 8-K
                                   May 5, 2004

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<Caption>

 Exhibit Number                     Description                                    Page No.
 --------------                     -----------                                    --------
                                                                           
    99.1                     Press Release dated May 3, 2004 -
                             The Shaw Group Inc. Announces Preliminary
                             Results of Tender Offer for its Outstanding
                             Liquid Yield Option(TM) Notes.
</Table>



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