Abstract: By using the second order Taylor series expansion, the original problem of structural optimization is reduced to a sequence of approximate problems. On the basis of the Kuhn-Tucher conditions, two iterative expressions for determining design variables and Lagrangian Multipliers are obtained. The convergence of this method is proved mathematically to be of the second order. The method can be used to solve problems with various kinds of behavioral constraints as long as the second Taylor series expansions of the functions involved in the given problem can be generated, and therefore it is of generalized and unified significance in theory and practice.Sensitivity analysis plays an important role in structural optimization. Based on the pseudo load concepts, general formulas for computing the first and second derivatives of behavioral parameters with respect to design variables are derived. By applying the Saint-Venant's principle to structures, the Hessian matrices are reduced to diagonal matrices, and the computational efficiency of design modification is enhanced accordingly.Several typical structures with stress, displacement and side constraints have been optimized to illustrate the power of this method. The results of the computations show that the method presented in this paper is quite efficient, and in general only two or three iterations are needed to meet the engineering accuracy requirement.