Exhibit 31.1

CERTIFICATION

    I, Herbert L. Henkel, certify that:

    1.      I have reviewed the Form 10-Q for the quarter ended September 30, 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: November 9, 2004                                                                                                  /S/ Herbert L. Henkel
                                                                                                                                                        Herbert L. Henkel
                                                                                                                                                        Principal Executive Officer