Solid propellants are highly filled elastomers used as propulsion medium. Because of the high volume filler fraction of 80% − 90%, several sizes of fillers are used and as a consequence of the complex microstructure the material presents important nonlinearities in the macroscopic behavior. An abrupt increase in the viscoelastic storage and loss modulus has been experimentally observed in [2]. The objective of this paper is to explore numerically a highly filled elastic composite under the assumptions of "rigid" fillers, an elastic matrix and large strains. The present numerical analysis is based on several artificially created microstructures. The results show the influence of the material behavior of the matrix on the global stiffness. The computed mechanical response is in agreement with experiment observations. The mechanical response of the composite under a uniaxial loading presents a linear and a nonlinear part. Both are analyzed to understand the microstructural effects that lead to the macroscopic behavior. The apparent modulus of the linear part increases with respect to the volume fraction of fillers and the stiffening effect occurring in the nonlinear part is not dependent of the matrix behavior.