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With the capacity of present-day digital computers, problems can be solved that were formerly approached only with great simplifications. This thesis advances the trend, relating the mechanical behavior of composite materials to their microstructure. The microstructure of particle reinforced composites is represented here by three-dimensional volumes, known as multiparticle cells, made up from a random distribution of spheres whose positions were generated from algorithms developed for this purpose. The cells were discretised and analysed by the finite element method, and the mechanical behavior of the composite was obtained by averaging the results provided by several dispersions for each microstructure.The numerical simulations provided an exact solution of a classical problem in solid mechanics: the elastic constants of a statistically homogeneous random distribution of rigid spheres and spherical voids embedded in a continuous matrix. This allowed an evaluation of the accuracy of the most important analytical models developed over the last forty years, and showed that the best results are obtained with the Torquato third order approximation.The simulation of the multiparticle cells also provided useful data of the elastoplastic behavior of a composite made of elastic spheres embedded in an elasto-plastic matrix.The results of the simulations were compared with those from mean-field secant modelswhich include the plastic deformation of the matrix by using the theory of total deformation plasticity-and it was found that these models provide better results when they use as the reference stress of the plastic strain in the matrix the equivalent stress computed from the second order moment of the stress tensor in the matrix. However, the mean-field models do not reproduce accurately the strain localisation in the matrix which appears at the onset of plasticity. The analysis of the stress microfields in the matrix provided by the simulations of the multiparticle cells indicated the cause of this limitation and the way to develop new approaches that would include the effect of the localisation.