Abstract: The necessity of the direct problem calculation in aerodynamic design of gas turbines with bowed and twisted blades is discussed and a practical direct problem calculation program is developed for the S 2 stream surface transonic flow in a multi stage gas turbine.In the calculation,the shape of the mean S 2 stream surface is taken as that of the blade mean camber surface which is modified properly to guarantee a reasonable S 2 stream surface shape,and the circulation is specified by the stream surface shape and the axial velocity.In the supersonic region,the density is corrected by means of the artificial compressibility treatment to make the calculation stable and the velocity is solved by density.This calculating method is applied to modification of a gas turbine.Meanwhile,the effects of different blade bowing methods on the radial distribution of gas parameters are analyzed.The calculation results demonstrate the improvement on the flow pattern in the turbine cascade with bowed and twisted blades and the necessity of the proof calculation with the direct problem method.Finally,several instructive opinions about the aerodynamic design of the bowed and twisted turbine blades are proposed.