The PISO Procedure is applied to numerically study inviscid compressible internal flows with and without shocks. The algorithm is applied in conjunction with a finite-volume technique for a body-fitted coordinate system. Computations are carried out for a quasi one dimensional convergent-divergent nozzle, a two dimensional circular arc bump, a two dimensional planar and axisymmetric RAMJET nozzle and a two dimensional planar and axisymmetric convergent-divergent nozzle. The results are compared with those of other numerical methods or experiments. It is found that the PISO procedure is stable for fairly large CFL numbers at low Mach number. However, the procedure becomes more restrictive for high Mach number flows.