Eaton Vance Floating-Rate & High Income Fund (EIFHX) N-CSRCertified annual shareholder report (management investment company)

Form N-CSR Item 19(b) Exhibit

CERTIFICATION PURSUANT TO

18 U.S.C. SECTION 1350,

AS ADOPTED PURSUANT TO

SECTION 906 OF THE SARBANES-OXLEY ACT OF 2002

The undersigned hereby certify in their capacity as Principal Financial Officer and Principal Executive Officer, respectively, of Eaton Vance Mutual Funds Trust (the “Trust”) that:

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