The applicability of generalized stochastic Petri nets (GSPNs) and other high-level modeling formalisms to real systems is often constrained by the explosion in the size of the underlying state-space representation. This paper describes a distributed program taking advantage of the large amount of memory and powerful computational resources of distributed computing systems to enable the construction of large state-space graphs generated by GSPN models. High state-space cardinalities and significant speedup with respect to sequential techniques are achieved by means of state space partitioning based on a distributed hashing function. The main algorithmic characteristics (global and local hashing and buffering of messages) are analyzed in detail and their effects are assessed by means of performance measurements on a PC cluster and a Cray T3D parallel machine. Performance results emphasize the good scalability with the number of processors of the proposed approach, even without fast interconnection networks. While the distributed reachability graph construction technique has been conceived for GSPN solution, the issues raised are relevant to other modeling systems whose common trait is the generation of state spaces with irregular and a priori unknown structure.