N-CSR Item 12(b) - Exhibits: Certifications

                            SECTION 906 CERTIFICATION

Pursuant to 18 U.S.C.ss.  1350,  the  undersigned  officers of Federated  Income
Securities Trust on behalf of Federated Fund for U.S. Government Securities (the
"Registrant"),   hereby  certify,  to  the  best  of  our  knowledge,  that  the
Registrant's  Report on Form  N-CSR for the  period  ended  March 31,  2005 (the
"Report")  fully complies with the  requirements  of Section 13(a) or 15(d),  as
applicable,  of the Securities and Exchange Act of 1934 and that the information
contained in the Report fairly presents, in all material respects, the financial
condition and results of operations of the Registrant.


Dated: August 15, 2005

/s/ J. Christopher Donahue

Title: President, Principal Executive Officer



Dated: August 15, 2005

/s/ Richard J. Thomas

Title: Treasurer, Principal Financial Officer

This  certification is being furnished solely pursuant to 18 U.S.C.ss.  1350 and
is not being filed as part of the Report or as a separate disclosure document.