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Most of existing formal models for BPEL based Web services composition are without description of dead-path-elimination semantics. There are Petri net based models describing the dead-path-elimination semantics, while the models are too big to handle large scale processes. In this paper, a new model called DPE net is advanced to describe the WS-BPEL process under the dead-path-elimination semantics. We give the DPE net models describing the basic control flow, relatively complete links semantics and dead-path-elimination semantics, and introduce how to analyze properties of the WS-BPEL process based on DPE reachability graph. The features of DPE net make the DPE net model for the WS-BPEL process smaller than the model based on P/T net. Moreover, the DPE reachability graph allows several transitions to be fired in one step, which reduces the reachability graph's size dramatically.