SECTION 906 CERTIFICATION

Pursuant to 18 U.S.C.ss. 1350, the undersigned officers of Federated Income
Securities Trust on behalf of Federated Intermediate Corporate Bond Fund,
Federated Short-Term Income Fund (the "Registrant"), hereby certify, to the best
of our knowledge, that the Registrant's Report on Form N-CSR for the period
ended April 30, 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: June 22, 2005

/s/ J. Christopher Donahue

Title: President, Principal Executive Officer



Dated: June 22, 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.