When optimizing corrugated flexure (CF) joints, most approaches for calculating the maximum stress on the CF beam depend on finite element analysis (FEA). The current paper introduces the design optimization for joints using CF units under stress constraints. The stress state is solved; based on that, the maximum displacement under stress constraints is deduced. The natural frequency formula of the translational joint is further derived from the results of the stiffness matrix. The stage configurations corresponding to the maximum displacement are optimized by restricting the off-axis/axial stiffness ratio and natural frequency of the joint. The optimal results of different types are validated by FEA and experiments.