Abstract: The Split-Coefficient Matrix (SCM) method is manipulated here for the numerical computation of Euler equations so as to simulate the two dimensional axisymmetric transonic nozzle flow.The coefficient matrix is splitted directly by a set of simplified formula.A second order accurate explicit scheme is constructed to compute inner grid points.The scheme is free of artificial viscosity and is economical in terms of computer memory.5151 grid points are embedded into the nozzle flowfield and the computational results are in good agreement with experiments.Once the flowfield is known,the Mach waves characteristic relations are numerically solved by Euler method.Based on the graphic output of the Mach number and Mach waves in nozzle,it is possible to demonstrate not only the formation and reflection of an oblique shock within a tested nozzle geometry but also its peculiar zonal distribution of expansion and compression waves.As a result excellent consistency between parameter distribution and waves construction is revealed.