As a structural object of Petri nets, siphons are significant in the analysis and control of deadlocks in a Petri net. However, some existing siphon computation methods are quite time-consuming. In this paper, based on incidence matrix manipulation, a new method is proposed to compute a set of siphons in a class of Petri nets called systems of simple sequential processes with resources (S3PR). The proposed method consists of two algorithms: 1) computation of an unmarked maximal siphon and 2) obtain minimal siphons from an unmarked maximal siphon. A flexible manufacturing systems (FMS) example is used to illustrate the proposed method.