Effective resolution for deadlock problems plays an important role in the operation of automated flexible manufacturing systems (FMS). Based on P-invariants and elementary siphons of Petri nets, a deadlock prevention policy is developed for a special class of Petri nets that can well model many FMS. Siphons in a plant net model are divided into elementary and dependent ones. For each elementary siphon, a monitor is added to the plant model such that the siphon is invariant-controlled. Our method guarantees that no emptiable control-induced siphon is generated due to the addition of the monitors. When all elementary siphons are controlled, the controllability of a dependent siphon is ensured by properly setting the control depth variables of its related elementary siphons. An FMS example is utilized to illustrate the proposed methods.