Exhibit 31.1

CERTIFICATION

    I, Herbert L. Henkel, certify that:

    1.     I have reviewed the Form 10-Q for the quarter ended March 31, 2004 of Ingersoll-Rand Company
            Limited;

    2.    Based on my knowledge, this 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 report;

    3.    Based on my knowledge, the financial statements, and other financial information included in this 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 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 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 report is being prepared;

                b.    Evaluated the effectiveness of the registrant's disclosure controls and procedures and presented
                       in this report our conclusions about the effectiveness of the disclosure controls and procedures,
                       as of the end of the period covered by this report based on such evaluation; and

                c.    Disclosed in this report any change in the registrant's internal control over financial reporting that
                       occurred during the registrant's most recent fiscal quarter 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  the
           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; and

                b.    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: May 5, 2004                                                              /s/ Herbert L. Henkel
                                                                                                  Herbert L. Henkel
                                                                                                  Principal Executive Officer