A systematic approach to socket shape design of a concave piston assembly for a high pressure hydraulic pump of an excavator is presented in this paper. A design model is given and a methodology of socket shape design is proposed. An axisymmetric rigid-plastic finite element method is employed for predicting the approximate socket shape formed by a rotary forming process as well as for simulating the test process for separating the shoe from the piston assembly designed. It is verified that the predictions are in good agreement with the experiments. The approach is successfully applied to developing an optimal concave piston assembly.