Abstract: A full mathematical model of optimal flow pattern design with engineering constraints was put forward,based on modern optimal control theory.An optimal flow pattern design was presented for optimizing meridional channel of axial flow turbine.According to integral optimization of turbine stages,a full physical model and mathematical expression were put forward for proposition of optimal flow pattern,including all performance parameters in turbine stages.This problem was further recast into a typical form control to maximize specific performance index such as work or efficiency of stage with given initial state,fixed terminal condition and constraints for part of state terminal variables.The program was also worked out according penalty function method and conjugate gradient method.The optimal distribution of C 1ur 1(r 1) was obtained according to constraint conditions and maximized objective function.