The neutron diffusion equation in reactor physics is solved on a multiple-instruction, multiple-data parallel computer network composed of five transputers. A parallel variant of the Schwarz alternating procedure for overlapping subdomains is used for domain decomposition. The parallel Schwarz algorithm with the concept of underrelaxation in pseudo-boundary conditions is applied to two types of reactor benchmark problems: fixed-source problems and eigenvalue problems. Results of parallel computation for these problems are reported and compared with results of sequential computation. The results show that a very high speedup can be achieved in fixed-source problems in spite of the small problem size and that a relatively high speedup, although lower than that of fixed-source problems, can be obtained in eigenvalue problems.