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, 2004 (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, 2004

/s/ J. Christopher Donahue

Title: President, Principal Executive Officer



Dated:  June 21, 2004

/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.