A major obstacle to topological optimization is that the optimal topology might correspond to a singular point in the design space. Despite its crucial importance, the phenomenon of singular optimal topologies is not well understood. The main objects of this paper are: (a) to clarify some properties of singular optimal topologies; (b) to discuss the effect of various constraints on the optimum; and (c) to present some design considerations related to the particular difficulties involved in topological optimization. It is shown that singular solutions are obtained mainly due to the nature of stress constraints. Displacement constraints might significantly affect the optimal cross-sections, but not necessarily the optimal topology. The effect of lower bounds on cross-sections is demonstrated and several two-stage solution procedures are discussed. © 1990 Springer-Verlag.