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, 2006 (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 21, 2006

/s/ J. Christopher Donahue
J. Christopher Donahue
Title: President, Principal Executive Officer



Dated: June 21, 2006

/s/ Richard A. Novak
Richard A. Novak
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.