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 June 30, 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
August 3, 2004

/S/ Timothy R. McLevish
Timothy R. McLevish
Chief Financial Officer
August 3, 2004