A method is presented for determining the shape of the detached shock andthe fiowfield in the supersonic entrance region on an arbitrary stream surface of revolution. The e-quation of characteristics and the corresponding equation of compatibility are derived. The shape of the detached shock obtained is taken as the initial- value curve to calculate the fiowfield in the supersonic entrance region by means of the method of characteristics. As an application of the present method, three stream surface of revolution in a transonic compressor roto have been calculated. The results show that the method is effective and useful to determine rapidly the shape of the detached shock wave as well as the fiowfield parameters in the supersonic entrance region. including the unique incidence angle in a supersonic or transonic compressor blade row.