AbstractA new method is developed in this paper for solving an aerodynamic hybrid problem of profile cascade on the S1 stream surface of revolution by employing a stream‐function equation on the non‐orthogonal co‐ordinate system. For this kind of problem, the shape of a portion of the blade profile is unknown. The remainder is determined by a given prescribed velocity distribution. Three examples, including two turbine cascades and a compressor cascade, have been carried out to examine this method. It is shown that the calculation method presented herein can be used as a powerful tool, together with the aerodynamic optimization method, for blade cascade design.