Abstract: Topology optimization design of continuum structures that can take account of stress and displacement constraints simultaneously is difficult to solve at present.The main obstacle lies in that,the explicit function expressions between topological variables and stress or displacement constraints can not be obtained using homogenization method or variable density method.Furthermore,large quantities of design variables in the problem make it hard to deal with by the formal mathematical programming approach.In this paper,a smooth model of topology optimization for continuum structures is established which has weight objective considering stress and displacement constraints based on the independent-continuous topological variable concept and mapping transformation method proposed by Sui Yunkang and Yang Deqing.Moreover,the approximate explicit expressions are given between topological variables and stress or displacement constraints.The problem is well solved by using dual programming approach,and the proposed element deletion criterion implements the inversion of topology variables from the discrete to the continuous.Numerical examples verify the validity of proposed method.