Abstract: The direct solution of three-dimensional flow in turbomachine are developed recently with the aid of computer and computational mathematics. In this papers, a new method is presented. The three-dimensional flow stream functions were introduced. The unified mathematical expressions for S1 and S2 relative stream surfaces model of Wu’s general flow theory for turbomachine were obtained. Further, the significance of stream surfaces was elucidated with these stream functions. Thickness of the stream surface appeared in the continuity equation of the stream surface model was derived in different way. These results coincided with those obtained from the stream surfaces model, and the physical significances of thickness of the stream surface were the same. Thus, the general flow pictures were obtained. And usually, the flow cases, such as arbitrary revolution surface, cylindrical surface, and axisymmetrical surface etc..met the special cases. The unified stream function equations governing the fluid flow on S1 and S2 relative stream surfaces were derived with the aid of the three-dimensional stream functions according to Wu’s basic aero-thermodynamic equations of flow in turbomachine. The significance and the approach of the iterative calculation of S1 and S2 stream surfaces can be easily understood. Further, the boundary conditions and the method of solution of the equations were discussed. So a new method of direct solution for three-dimensional flow in turbomachine is presened here. In this way, the both stream functions Ψ1 andΨ2, are calculated on computational nodes in three-dimensional space. The values of Ψ1 andΨ2 are obtained by iterative solution of two simultaneous stream function equations. All the aero-thermodynamic parameters can be obtained, by the general formulae. This method is different from the solution of three-dimensional flow equations expressed with respect to velocity components. In the latter case, three or more unknown functions must be calculated. This new method is probably more easy than the conventional methods in order to get the integral three-dimensional flow in turbomachine with the aid of computers.