Exhibit 23

CONSENT OF INDEPENDENT AUDITORS

We consent to the incorporation by reference in the registration statement (No. 333-74163) on Form S-3 and registration statement (No. 333-49912, 33-24415, 33-62541, 333-64661, 333-30528 and 333-105033) on Form S-8 of Sigma-Aldrich Corporation of our report dated February 6, 2004 with respect to the consolidated balance sheets of Sigma Aldrich Corporation as of December 31, 2003 and 2002, and the related consolidated statements of income, stockholders’ equity and cash flows for each of the years in the three-year period ended December 31, 2003, which report appears in the December 31, 2003 annual report on Form 10-K of Sigma Aldrich Corporation.

Our report refers to a change in accounting in 2002 for goodwill and other intangible assets.

/S/    KPMG LLP

St. Louis, Missouri

March 11, 2004