The development of a parallel stochastic cellular automata model for neutron transport is presented. The model is derived from neutron physics and is implemented on a 2048 processor singleinstruction multiple-data architecture MasPar computer. Purely absorbing and purely fissioning onedimensional benchmarks are performed against analytical solutions. Favorable results from these two benchmarks motivated the performance of three other test cases. Results for a two-dimensional scattering-absorbing case and a one-dimensional time-dependent case compared fairly well qualitatively with literature results. Also, results from a one-dimensional, two-group case compared somewhat favorably, but the scheme used was deemed not efficient enough without modification.