Methods for simulating multistage interconnection networks using massively parallel SIMD computers are presented. Aspects of parallel simulation of interconnection networks are discussed and different strategies of mapping the architecture of the network to be simulated onto the parallel machine are studied and compared. To apply these methods to a wide variety of network topologies, the discussions are based on general interconnection network and switch box models. As case studies, two strategies for mapping synchronous multistage cube networks on the MasPar MP-1 SIMD machine are explored and their implementations are compared. The methods result in a simulator implementation with which 109 data packets can be simulated in 40 minutes on the MasPar system.