Stress constrained topology optimization problem has notbeen paid the same attention as the minimum compliance problem in theliteratures. The traditional minimum compliance formulations offer someobvious advantages to avoid dealing with a large number of highly non-linearconstraints. This could be considered crucial, if one takes into account thelarge number of design variables, i.e. inherent to topology optimization.However, one can also argue that this gives rise to several importantdrawbacks since no constraints are imposed on stresses and displacements,for example, multiple load cases cannot be considered; different solutionsare obtained for different restrictions; the final design could beunfeasible in practice. This paper deals with topology optimization ofcontinuum structures with stress and displacement constraints or with onlystress constraints, based on the ICM method and the evolutionary structuraloptimization method. New displacement and stress constraint limits areformed and introduced into the optimization model at the beginning of eachoptimization iteration sub-loop, so that moving limits of design variablescan be easily constructed. Instead of all stress constraints, only the mostpotential effective stress constraints are considered. In this way, stresssensitivity analysis is much less costly. Moreover, the element deletion anda set of structural optimization strategies are given. In order to make thestructure optimized be non-singular and the proposed method be of elementrestorable functions, some elements with artificial material property areinserted around the cavities and boundaries of the structure optimized.Meanwhile, an equivalent topological optimization model is developed.Incorporating displacement and stress sensitivity analyses, a new continuumstructural topological optimization method is also proposed. Two simulationexamples demonstrate that the proposed method is of validity andeffectiveness.