Abstract: Viscous compressible flow around a circular cylinder is numerically simulated. The inflow Mach numbers and Reynolds numbers of the flow are from 0.1 to 0.9 and 103 to 8.4 x 106 respectively. Two-dimensional time averaged Navier-Stocks equations were numerically Solved. The Beam-Warning type numerical method was employed on two different C- and O-type meshes. The effects of Mach and Reynolds numbers on the flow parameters such as drag and lift coefficients and the formation and growth of the vortices were investigated. It is found that for mach numbers above about 0.6, the flow parameters become independent of Reynolds number and at about this Mach numbers. But as Mach number becomes greater than 0.8(0.8<M<1.0), the flow becomes independent of Mach number. In some cases, where experimental results were available, the results were compared and good agreement was obtained.