Abstract: This paper is concerned with three teeth fir-tree tenon/mortise structure, and a detailed method of shape optimal design is proposed by means of an effective solution of the design variables and constraint variables, which has evident engineering significance in designing and remodeling the tenon/mortise structure. With feature-based modeling method, geometry shape representation is undertaken for the 2D trapezoidal tenon/mortise structure, and then the parametric model is established. Sensitivity analysis is made available using the Gradient-based method which extracts design variables from a large number of parameters. Also constraint variables are obtained based on engineering experience and stressing standards. At last, as the objective function, the maximum equivalent stress of trapezoidal tenon/mortise structure decreases by 12% and is verified by photo-elastic experiment, proving the validity of the optimization results.