Abstract: An analytical method of shape optimization is put forward for two-dimensional elastic contact problems with boundary element method.Choice of the design variables and a method of shape description,as well as determination of target function and restrain conditions in two-dimensional elastic contact problems are considered.The numerical examples are carried out on the sensitivity and shape optimaization.Furthermore,the shape optimization analysis of the the fir-tree tenon/mortise in an aeroengine is carried out.