**                                                                                    Exhibit 31.1**

** **

**CERTIFICATION **

 I, Herbert L. Henkel, certify that:

1.   I have reviewed the annual report on Form 10-K ofIngersoll-Rand Company Limited;

2.   Basedon my knowledge, this report does not contain any untrue statement of amaterial fact or omit to state      a material fact necessary to make the statementsmade, in light of the circumstances under which such      statements were made, notmisleading with respect to the period covered by this report; 

3.   Basedon my knowledge, the financial statements, and other financial informationincluded in this report,      fairly present in all material respects the financialcondition, results of operations and cash flows of the      registrant as of, andfor, the periods presented in this report;

4.   Theregistrant's other certifying officer and I are responsible for establishingand maintaining disclosure       controls and procedures (as defined in Exchange ActRules 13a-15(e) and 15d-15(e)) for the registrant       and have:

            a.   Designedsuch disclosure controls and procedures, or caused such disclosure controls and                   procedures to be designed under our supervision, to ensure that materialinformation relating to the                   registrant, including its consolidatedsubsidiaries, is made known to us by others within those                   entities, particularlyduring the period in which this report is being prepared;

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

            c.   Disclosedin this report any change in the registrant's internal control over financialreporting that                   occurred during the registrant's most recent fiscal quarter thathas materially affected, or is                   reasonably likely to materially affect, theregistrant's internal control over financial reporting; and

5.   Theregistrant's other certifying officer and I have disclosed, based on our mostrecent evaluation of       internal control over financial reporting, to theregistrant's auditors and the audit committee of the       registrant's board of directors (or persons performing theequivalent functions):

            a.  Allsignificant deficiencies and material weaknesses in the design or operation ofinternal control                 over financial reporting which are reasonably likely toadversely affect the registrant's ability to                 record, process, summarize andreport financial information; and

            b. Anyfraud, whether or not material, that involves management or other employees whohave a                 significant role in the registrant's internal control over financialreporting.

Date: February 26, 2004                                              /s/Herbert L. Henkel                                                                                    Herbert L. Henkel                                                                                    PrincipalExecutive Officer