In this study, MIMD parallel computation of coupled non-linear partial differential equations governing the mass and momentum conservation of a 3D viscous incompressible unsteady flow on distributed memory-based vector parallel processing system (VPP700) under UXP/VPPF90 has been discussed. The parallel numerical implementation is based on a time accurate cell centered finite volume method in conjunction with Roe's flux difference splitting of non-linear terms and pseudo-compressibility technique. Data flow graphs necessary for combined parallelization and vectorization have been generated to provide a logical basis for parallel code development. The performance of the parallel implementation measured in terms of speedup and efficiency factors is found to be good. The parallel code is tested on three test problems of practical significance.