Topology optimization is an optimization technique used to find optimal material distribution with in a given design domain under applied loads and boundary conditions. Most of the developments in structural topology optimization have been formulated and solved for minimizing compliance. The absence of considering the displacement and stress constraints in the formulation and solution of topology optimization problems may lead the unfeasible optimal solutions where stress and displacement constraints are crucial criteria for the design considered. To include these two crucial elements in the optimization process some efforts have been devoted to formulate and solve the optimization problem by including stress constraints. Though considering the stress constraint in the optimization model is closer to the engineering point of view it facing three main challenges associated with the constraints. This paper aims to explore and discuss the three challenges in stress based topology optimization along with the proposed solutions. © 2006-2016 Asian Research Publishing Network (ARPN). All rights reserved.