The paper deals with multi-objective Topological Optimum Design (TOD) problems. Considered optimization criteria are the minimization of both the mass of the structure and its maximal displacement under a prescribed loading. Multi-objective evolutionary algorithm using Voronoi representation are applied on the cantilever plate, the popular benchmark problems of TOD. The results are discussed in the light of the single objective approaches used in previous works: whereas the quality of the result is very similar, the number of Finite Element Analyzes needed to obtain a full set of trade-off structures by the multi-objective method is more or less the same that needed to obtain only one solution using a single-objective algorithm with a limit on the maximal displacement: This makes multi-objective approach extremely interesting for solving real life TOD problems where the evaluation cost is usually quite high while the possibility of making of a well justified choice of definitive design is very important.