Abstract: Because of the local characteristics of element stresses, the corresponding structural topology optimization model has too many constraints. Although a globalization method can dramatically reduce the number of constraints in the optimization model, there exist a few elements whose stresses exceeds the allowable stress of materials in the optimized topology. For stress topology optimization problems of continuum structures, this paper aims to overcome the problems of stress over-limit and to improve the solve efficiency. The multiplier method and sequence quadratic programming (SQP) method are proposed. And an aggregation model, called as the m-model in the globalization blend method (named by the globalization-aggregation method), is solved by the two proposed methods. And the solve efficiency of the two proposed methods are compared with the moving asymptote method (MMA) which solves a series of first-order approximated model. On this basis, the SQP method, the most effective method of solving m-model, is adopted to blend with globalization method to form the globalization blend method, which is adopted to solve the structural volume minimization model under stress constraints (named by the s-model). The globalization blend method is compared with the previous globalization method. The results show that: (1) among the three methods of solving the m-model, the solve efficiency of the multiplier method and SQP method is much higher than that of the MMA method. And the solve efficiency of the SQP method is slightly higher than that of the multiplier method. (2) Although the solve efficiency of the globalization blend method is similar to that of the globalization method, the globalization blend method completely avoids the phenomenon of element stress over-limit. In the condition that all stress constraints are satisfied, the resulting optimized topology obtained by the globalization blend method is lighter than that of the globalization method. The globalization blend method has stronger ability to find the optimal solution.