**Exhibit 31.1**
**CERTIFICATION PURSUANT TO SECTION**
**302 OF THE SARBANES-OXLEY ACT OF 2002**
I, Andrew A. Barnard, President and Chief Executive Officer of Odyssey Re Holdings Corp., certifythat:
1.  I have reviewed this annual report on Form 10-K of the registrant, Odyssey Re Holdings Corp.; 2.  Based on my knowledge, this annual report does not contain any untrue statement of a materialfact or omit to state a material fact necessary to make the statements made, in light of thecircumstances under which such statements were made, not misleading with respect to the periodcovered by this annual report; 3.  Based on my knowledge, the financial statements, and other financial information included inthis annual report, fairly present in all material respects the financial condition, resultsof operations and cash flows of the registrant as of, and for, the periods presented in thisannual report; 4.  The registrant’s other certifying officer and I are responsible for establishing andmaintaining disclosure controls and procedures (as defined in Exchange Act Rules 13a-15(e) and15d-15(e)) and internal control over financial reporting (as defined in Exchange Act Rules13a-15(f) and 15d-15(f)) for the registrant and we have: (a)  designed such disclosure controls and procedures, or caused such disclosure controls andprocedures to be designed under our supervision, to ensure that material information relatingto the registrant, including its consolidated subsidiaries, is made known to us by otherswithin those entities, particularly during the period in which this annual report is beingprepared; (b)  designed such internal control over financial reporting, or caused such internal control overfinancial reporting to be designed under our supervision, to provide reasonable assuranceregarding the reliability of financial reporting and the preparation of financial statementsfor external purposes in accordance with generally accepted accounting principles; (c)  evaluated the effectiveness of the registrant’s disclosure controls and procedures andpresented in this annual report our conclusions about the effectiveness of the disclosurecontrols and procedures, as of the end of the period covered by this annual report based onsuch evaluation; and (d)  disclosed in this annual report any change in the registrant’s internal control overfinancial reporting that occurred during the registrant’s fourth fiscal quarter that hasmaterially affected, or is reasonably likely to materially affect, the registrant’s internalcontrol over financial reporting; and 5.  The registrant’s other certifying officer and I have disclosed, based on our most recentevaluation of internal control over financial reporting, to the registrant’s auditors and theaudit committee of the registrant’s board of directors (or persons performing the equivalentfunctions): (a)  all significant deficiencies and material weaknesses in the design or operation of internalcontrol over financial reporting which are reasonably likely to adversely affect theregistrant’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 asignificant role in the registrant’s internal control over financial reporting.        Date: March 7, 2005 By:  /s/ ANDREW A. BARNARD    President and Chief Executive Officer