This paper applies a theoretical model developed recently to calculate the flow-instability inception of an axial transonic single stage compressor. After several calculation methods are compared, the singular value decomposition method is adopted to solve the resultant eigenvalue problem in which the involved matrix is rather large due to multistage configuration. The onset point of flow instability is judged by the imaginary part of the resultant eigenvalue. The effect of flow compressibility on the stall onset point calculation for the transonic rotor is studied. It is shown that the compressibility of flow perturbation plays a major role in computing high speed compressor flow stability.