Exhibit 32

Section 1350 Certifications
Pursuant to Section 906 of the Sarbanes-Oxley Act of 2002
(Subsections (a) and (b) of Section 1350, Chapter 63 of Title 18, United States Code)
 

        Pursuant to Section 906 of the Sarbanes-Oxley Act of 2002 (Subsections (a) and (b) of Section 1350,
        Chapter 63 of Title 18, United States Code), each of the undersigned officers of Ingersoll-Rand
        Company Limited (the Company), does hereby certify that:

        The quarterly Report on Form 10-Q for the quarter ended March 31, 2004 (the Form 10-Q) of the
        Company fully complies with the requirements of section 13(a) or 15(d) of the Securities Exchange Act of
        1934 and information contained in the Form 10-Q fairly presents, in all material respects, the financial
        condition and results of operations of the Company.

        /s/ Herbert L. Henkel            
        Herbert L. Henkel
        Chief Executive Officer
        May 5, 2004

        /s/ Timothy R. McLevish      
        Timothy R. McLevish
        Chief Financial Officer
        May 5, 2004