Abstract: Optimality Criteria Method (OCM) has been successfully used in the optimum design of fiber reinforced composite structures with stress and displacement constraints.The default of OCM for this kind problem is that its efficienty is not very high and the interation history is rather long.In this paper,reciprocal variables have been used and the original problem has been replaced by a dual problem in quadratie form and by SQPM,and then the dual problem of mathematical programming has resulted in a very efficient method of composite structural ooptimization.The results of comparison of the two methods in one example are presented.The project is suported by the Science Fund of the Chinese Academy of Science.