A description of a system which provides for the concurrent execution of stochastic simulation applications is presented. The EcliPSe system provides high-level simulation primitives that enable common sawlation tasks. An application programmer describes the simulation process in terms of these primitives using a sequential computation model. The system transparently replicates appropriate sections of the simulation when the program is executed on a concurrent system. By binding to machine-dependent versions of the EcliPSe library, the simulation program can execute without modification on a variety of architectures including uniprocessors, hypercubes, shared-memory machines and loosely coupled networks. In those experiments conducted, near-linear speed-ups were obtained. The main design aspects of the system, salient implementation features and performance figures for some simulation applications are presented. The usefulness of the system for more general applications is also discussed.