This chapter introduces the stochastic Petri nets. Stochastic Petri nets is a term that denotes a family of stochastic models that is part of a larger family of behavioral models named Petri nets. Immediate transitions are graphically represented by thin black rectangles, timed exponentially distributed are depicted by white rectangles, deterministic timed transitions are represented by thick black rectangles, and timed generically distributed gray rectangles denote transitions. An important issue that arises at every transition firing is concerned with the memory policy of transitions. The main concern is how to set the transition timers when a marking change occurs, possibly modifying the enabling of transitions. The memory policies assigned to transitions are: restart and continue. Elimination on the fly is efficient concerning memory requirements because vanishing markings are not stored at all.