Abstract: This paper provides a multi-objective optimum design method for a radial-axial flow turbine stage. The method takes the parameters in mean radius,α₁、β₂、μ、and m=u₂/w₂cosβ₂2, and the criteria of blade twist at the outlet of the blades as design variables, and selects the internal efficiency in the design conditions and the total weight of the turbine stage as objective functions. The model presented is a nonlinear multi-objective programming problem of two objective functions with 29 constrained functions and 6 variables. The mathematical model for optimization and some analytical results of single- and multi-objective optimization for a variety of twisted blades are also presented in this paper. The numerical results demonstrate the validity and effectiveness of the method.