A numerical analysis of shock wave/boundary layer interaction in transonic^{ersonic axial flow compressor cascade has been performed by using a characteristics upwind Navier-Stokes method with various turbulence models. Two equation turbulence models were applied to transonic}supersonic flows over a NACA 0012 airfoil. The results are superion to those from an algebraic turbulence model. High order TVD schemes predicted shock wave/boundary layer interactions reasonably well. However, the prediction of SWBLI depends more on turbulence models than high order schemes. In a supersonic axial flow cascade at M=1.59 and exit/inlet static pressure ratio of 2.21, k-$omega$ and Shear Stress Transport (SST) models were numerically stables. However, the k-$omega$ model predicted thicker shock waves in the flow passage. Losses due to shock/shock and shock/boundary layer interactions in transonic/supersonic compressor flowfields can be higher losses than viscous losses due to flow separation and viscous dissipation.