Abstract: It assesses the Rayleigh inverse-iteration method and boundary layer asymptotic expansion method, and uses them into the stability equations of compressible boundary layer and the numerical method for forecasting the transition point. It gives also a stability analysis on the first mode of the boundary layer of flat plane and a forecasting of transition point. Results are discussed and compared with observations.

Key words: compressible boundary layer, stabicity transition, Rayleigh inverse iteration