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Supersonic ows past a blunt body in air and in water are numerically investigated by using a high-resolution Euler/Navier-Stokes solver. The numerical method used is a fourth-order Runge-Kutta method for time integration with a fth-order weighted essentially nonoscillatory scheme for discretizing the convective terms and central differencing for the viscous terms. The inviscid-and viscous-ow results are compared. It was found that the inviscid-ow model is able to predict reasonably accurate ow elds such as the bow shock and sonic-line locations. Moreover, for the case of medium water the bow-shock location is farther upstream, and the sonic line is farther downstream compared with the case of medium air.