A number of scientific models are discussed that possess a high degree of inherent parallelism. For simulation purposes this is exploited by employing a massively parallel SIMD (single instruction multiple data) computer. The authors describe one such computer, the distributed array processor (DAP), and discuss the optimal mapping of a typical problem onto the computer architecture to best exploit the model parallelism. By focusing on specific models currently under study, they exemplify the types of problems which benefit most from a parallel implementation. The extent of this benefit is considered relative to implementation on a machine of conventional architecture.>