The objectives of this paper are to present the development and implementation of parallel numerical methods for inviscid and viscous compressible flows. A flux vector splitting scheme and a Riemann solver were used to discretize the Euler and Navier-Stokes equations. Furthermore, an implicit unfactored procedure with Gauss-Seidel relaxation was used to solve the equations in time dependent form. Acceleration of the convergence was achieved by the local solution method and the mesh sequencing technique. Grid partitioning was utilized for the parallelization of the methods. Calculations were performed on various parallel platforms and factors that can influence the parallel performance, such as numerical method, acceleration procedure, grid size, and interprocessor communication were investigated.