**                                                                                    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 for the year ended December 31, 2004;

    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)) and internal control over financial reporting(as defined in Exchange Act Rules 13a-15(f)             and 15d-15(f)) for the registrantand have:

                a.       Designedsuch disclosure controls and procedures, or caused such disclosure controls andprocedures 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.      Designedsuch internal control over financial reporting, or caused such internal controlover financial reporting to be designed under                         our supervision, to providereasonable assurance regarding the reliability of financial reporting and thepreparation of financial                         statements for external purposes in accordance withgenerally accepted accounting principles;

                c.       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

                d.      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: March 14, 2005                                                                                                       /s/Herbert L. Henkel                                                                                                                                                      Herbert L. Henkel                                                                                                                                                      PrincipalExecutive Officer