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Exhibit 31.1


CERTIFICATION PURSUANT TO SECTION 302 OF THE SARBANES-OXLEY
ACT OF 2002






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| | 1. | I have reviewed this quarterly report on Form 10-Q of the
    registrant, Odyssey Re Holdings Corp.;                                                                                                                                                                                                                                                       
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| | 2. | Based on my knowledge, this quarterly 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 quarterly
    report;         
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| | 3. | Based on my knowledge, the financial statements, and other
    financial information included in this quarterly 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 quarterly report;                                
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| | 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)) and internal control over financial reporting (as
    defined in Exchange Act Rules 13a-15(f) and 15d-15(f)) for
    the registrant and we have:



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| | (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 quarterly report is being prepared;
|
| | (b) | designed such internal control over financial reporting, or
    caused such internal control over financial reporting to be
    designed under our supervision, to provide reasonable assurance
    regarding the reliability of financial reporting and the
    preparation of financial statements for external purposes in
    accordance with generally accepted accounting principles;                 
|
| | (c) | evaluated the effectiveness of the registrants disclosure
    controls and procedures and presented in this quarterly report
    our conclusions about the effectiveness of the disclosure
    controls and procedures, as of the end of the period covered by
    this quarterly report based on such evaluation; and                                                                                     
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| | (d) | disclosed in this quarterly 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                                                                



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| | 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):



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| | (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
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| | (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.                                                                                                       

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|Date: May 9, 2005 |  | By /s/ Andrew A.
    BarnardPresident
    and Chief Executive Officer