Abstract A finite Analysis Method is further extended to numerical calculation of viscous compressible turbulent flow on the basis of experience of incompressible turbulent flow calculation.The viscous compressible turbulent flow fields in a single and a tandem cascades with Mach number up to 0 72 are numerically studied in a curvilinear coordinate system by means of the Finite Analysis Method.The study shows that the Finite Analysis Method has good numerical stability and accuracy,and it is suitable for viscous compressible turbulent flow calculation.