It aims to extend high resolution AUSMPW shock capturing scheme to the multidimensional hyperbolic conservation laws in curvilinear coordinates.The third order MUSCL shceme with Van Leer limiter is used to extend the basic first order AUAMPW scheme to third order spatial accuracy for all test cases.The equations are discretized by using a finite volume method.The present scheme combined with the LU SGS scheme is applied to compressible inviscid and viscous flows.The computed results are compared with the experimental data or the other numerical results available in literature and good agreements between them are obtained.The AUSMPW scheme is also compared with CD, TVD, FVS and FDS schemes.