Although the phenomenon of stress concentration is of paramount importance to engineers when they are designing load-carrying structures, stiffness is often used as the solely concerned objective or constraint functional in the studies of optimal topology design of continuum structures. Sometimes this will lead to optimal designs with severe stress concentrations that may be highly responsible for the fracture, creep, and fatigue of structures. The aim of the present work is to develop some effective numerical techniques for designing stiff structures with less stress concentrations. This is achieved by introducing some specific stress measures, which are sensitive to the existence of high local stresses, in the problem formulation and resolving the corresponding optimization problem numerically in a level set framework. Our study indicates that with use of the proposed numerical schemes, some intrinsic difficulties in stress-related topology optimization of continuum structures can be overcome in a natural way. Copyright © 2012 John Wiley & Sons, Ltd.