Abstract: In this paper,the boundary element method is combined with the impr-oved complex optimal method,and the complicated nonlinear implicit cons-traints are expanded point by point to linear constraints,thus,the check process of stress constraints at apexes is simplified and the volume of co-mputation reduced.Optimal mathematical models are provided for the conc-rete gravity dam and the hollow gravity dam.Calculation is performed with the present method for the optimal shape of a gravity dam.Compared the original shape,the optimal shape can save the volume of concrete by 20%.