Cycle is one of the most fundamental graph classes. For a given graph, it is interesting to find cycles of various lengths as subgraphs in the graph. The Cayley graph Cay(e., S) on the symmetric group has an important role for the study of Cayley graphs as interconnection networks. In this paper, we show that the Cayley graph generated by a transposition set is vertex-bipancyclic if and only if it is not the star graph. We also provide a necessary and sufficient condition for Cay(n, S) to be edge-bipancyclic. (C) 2009 Elsevier B.V. All rights reserved.