Abstract: One semi-actuator stability model for rotating stall considering in-passage shock wave was developed based on a three-dimensional compressible theory,and it was evaluated to be effective by comparing the results with experiments.Winding number integral method has been developed to solve the roots of complex functions for a long time,although it is not widely used,in some way,it is more stable than Newton-Raphson iteration method.The author used this approach to solve the eigen equation of the transonic stability model,and it is strongly recommended to extend its use in other fields because of its advantages over other methods.