EXHIBIT 32.1

                            CERTIFICATION 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 Quarterly Report of Chicago Bridge & Iron Company N.V.
(the "Company") on Form 10-Q for the period ending March 31, 2004 as filed with
the Securities and Exchange Commission on the date hereof (the "Report"), I,
Gerald M. Glenn, Chief Executive Officer of the Company, 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.



/s/ GERALD M. GLENN
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Gerald M. Glenn
Chief Executive Officer
May 10, 2004