This paper is devoted to minimum stress design instructural optimization. We propose a simple andefficient numerical algorithm for shape and topologyoptimization based on the level set method coupledwith the topological derivative. We compute ashape derivative, as well as a topological derivative,for a stress-based objective function. Using anadjoint equation we implement a gradient algorithmfor the minimization of the objective function.Several numerical examples in 2-d and 3-d are discussed.