Through analyzing the motion characteristics of bird-like flapping flight, it is considered that the wing angular acceleration is equal to zero at the point of maximum angular speed. Thus, the flapping flight is equivalent to a uniform rotating motion which can be analyzed by using the stream surface theory of turbomachinery during a micro period of time. In this article, the N-S equations of the motion are expanded in a non-orthogonal curvilinear coordinate system, and simplified on stream surfaces of the flapping flight model. By using stream function method, the three-dimensional unsteady flow equations are simplified as a two-order partial differential equation with variable coefficients eventually and the equation’s iterative solving method on S1 and S2 stream surfaces of the flapping flight model is presented. Through expanding the relatively steady equations of flapping flight at an arbitrary time point of a stroke on meridional plane of the flapping flight model, it can use a relatively steady motion to approximate the real flapping flight at that time point, and analyze the flow stability influenced by the wing’s flexibility. It can be seen that the wing flexibility is related to the higher pressurization capacity and the flow stability, and the pressurization capacity of flexible wing is proportional to the angular speed, angular distortion rate and radius square. Through analyzing the motion characteristics of bird-like flapping flight, it is considered that the wing angular acceleration is equal to zero at the point of maximum angular speed. Thus, the flapping flight is equivalent to zero at the point of maximum angular speed. the stream surface theory of turbomachinery during a micro period of time. In this article, the NS equations of the motion are expanded in a non-orthogonal curvilinear coordinate system, and simplified on stream surfaces of the flapping flight model. , the three-dimensional unsteady flow equations are simplified as a two-order partial differential equation with variable coefficients eventually and the equation’s iterative solving method on S1 and S2 stream surfaces of the flapping flight model is presented. flight at an arbitrary time point of a stroke on meridional plane of the flapping flight model, it can use ar elatively steady steady to approximate the real flapping flight at that time point, and analyze the flow stability influenced by the wing’s flexibility. It can be seen that the wing flexibility is related to the higher pressurization capacity and the flow stability, and the pressurization capacity of flexible wing is proportional to the angular speed, angular distortion rate and radius square.