This paper presents the development of a parallel multiblock method for three-dimensional incompressible flows. Parallelization of the method is obtained using shared-memory, as well as message-passing models. The two models are compared for their efficiency. Results are also presented on different multiple instruction multiple data systems. Investigations of the parallel performance using different grid sizes and number of processors is obtained. The solver is based on a third-order characteristic-based upwind method. The artificial compressibility formulation is used for coupling the continuity with the momentum equations. The time integration is obtained by an explicit Runge-Kutta scheme.