Abstract: In order to improve aerodynamic design of a compressor,one way is to find out how to weaken the strength of shock wave in a transonic cascade passage and how to incorporate the method used in the available compressor design system.A numerical method for weakening shock wavt in a transonic cascade flow field is presented in this paper,which is based on direct problem calculation and modification of an existing profile surface to weaken shock waves.The line-relaxation method is adopted to calculate a transonic flow field in a cascade.Then two versions of algorithms are considered to weaken shock waves.The characteristic marching is adopted in embedded supersonic region to calculate shock strentgh in the first version.In the second version,the line relaxation method is adopted to calculate shock strentgh in the whole flow field.The profile suction surface is modified by an optimization technique.Two numerical examples of transonic cascades are presented.In one of them the incoming Mach number is less than 1.0 and in another more than 1.0.The results of these examples show that the effects of weakening shock wave appear quite evident.This method is feasible provided it is incoporated in an available compressor design system.