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40      The May Department Stores Company Exhibit 31.1 Certification I, John L. Dunham, certify that:  1.
    I have reviewed this annual report on Form 10-K of The May Department Stores Company;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)) and internal control over financial reporting (as
defined in Exchange Act Rules 13a-15(f) and 15d-15(f)) 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)
    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 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; andd)
    Disclosed in this report any change in the registrants internal control over financial
reporting that occurred during the registrants fourth 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; andb)
    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: March 25, 2005
    
    /s/
    
    John L. DunhamJohn L. Dunham

Chairman, President, and
Chief Executive Officer