An evaluation of eight upwind schemes of Roe, van Leer, AUSM-type and CUSP-type is presented in order to assess their performance for entropy condition and discontinuities. The inviscid shock tube problem is tested to examine the entropy condition of upwind schemes for nonlinear Euler equations. The numerical results agree with theoretical results perfectly. It is observed that these upwind schemes allow expansion shock in the vicinity of sonic point when the first order accurate discretization is used and they violate the entropy condition. A blast wave impinging on a 2D compression wedge is also tested for these schemes on comparing the quality of the discontinuities captured. The numerical results agree with experiment results well at discontinuities, but the differences at contact discontinuities cannot be neglected. Better results of the schemes of Roe, van Leer and CUSP-type are obtained at contact discontinuities than the AUSM-type schemes.