This work proposes the use of the MSAA stochastic optimization technique to replace the optimality criterion used in the topology optimization method proposed by Andreassen. To evaluate and validate the MSAA performance we studied three plane elasticity problems reported in the literature. Each problem was analyzed with three different finite element mesh types in order to compare the results obtained in terms of topology, strain energy value and average runtimes. It was established that the procedure involving the MSAA, yields lower computational times in problems with more refined meshes. Finally, the material distribution and the energy values obtained were similar to those reported in the work of Andreassen giving validity to the work presented here.