EXHIBIT 32

CERTIFICATION PURSUANT TO
18 U.S.C. SECTION 1350,
AS ADOPTED PURSUANT TO
SECTION 906 OF THE SARBANES-OXLEY ACT OF 2002

     In connection with the Quarterly Report of Apex Silver Mines Limited (the “Company”) on Form 10-Q for the period ended March 31, 2004, as filed with the Securities and Exchange Commission on the date hereof (the “Report”), each of the undersigned hereby certifies, pursuant to 18 U.S.C. §1350, as adopted pursuant to § 906 of the Sarbanes-Oxley Act of 2002, that:

     (1) The Report fully complies with the requirements of section 13(a) or 15(d) of the Securities Exchange Act of 1934; and

     (2) The information contained in the Report fairly presents, in all material respects, the financial condition and result of operations of the Company.

/s/ Keith R. Hulley

Keith R. Hulley
Chief Executive Officer
August 6, 2004

/s/ Mark A. Lettes

Mark A. Lettes
Chief Financial Officer
August 6, 2004

     A signed original of this written statement required by Section 906 has been provided to Apex Silver Mines Limited and will be retained by Apex Silver Mines Limited and furnished to the Securities and Exchange Commission or its staff upon request.