Abstract: It is necessary to limit maximum nominal stress for engineering structural design generally, so as to avoid that the failure of fracture or fatigue occurs. Topology optimization approach is a feasible strategy. The conventional bi-evolutionary structural optimization (BESO) method cannot effectively address the topology optimization problem with stress constraint. To overcome this limitation, this paper suggests an improved BESO method for stress-constrained topology optimization, in which the minimum compliance design problem with volume and stress constraints is considered. A global stress measure based on the K-S function is introduced to reduce the computational cost associated with the local stress constraint. Meanwhile, the stress constraint function is added to the objective function by using the Lagrange multiplier method. Moreover, the appropriate value of the Lagrangian multiplier is then determined by a bisection method so that the stress constraint is satisfied. The model of BESO method for solving stress-constrained topology optimization and its sensitivity analysis are detailed. Finally, three typical topology optimization examples are performed to demonstrate the validity of the present method, in which the stress constrained designs are compared with the traditional stiffness based designs to illustrate the merit of considering stress constraint. The optimized results indicate that the improved BESO method, as a robust algorithm with stable iterative history, achieves an ambiguous topology with clearly defined boundaries, and realizes a design that effectively reduces stress concentration effect at the critical stress areas.