We investigate numerically via finite element (FE) simulations and analytically the nonlinear behavior of a soft matrix comprising a large volume fraction (up to 55%) of monodisperse spherical inclusions, which can be either rigid particles or voids. To address the issue of severe mesh distortion at large strains, we employ a successive remeshing and solution mapping technique that allows us to achieve a large macroscopic deformation, with the maximum attained stretch being at least two to three times when compared to that without remeshing. A general algorithm allowing to read complex arbitrary particle geometries is proposed and implemented allowing to remesh a finitely strained domain with randomly distributed inclusions of arbitrary shape. The present simulation results for a neo-Hookean elastic matrix filled with rigid particles show that the nonlinear stress-stretch uniaxial tension response can be well approximated by a neo-Hookean material with an effective shear modulus that depends on the volume fraction of the inclusions. Additionally, a study of the number of particles demonstrates that sixty four monodisperse spheres is a good compromise to reach accurate results for large deformations and maintain a reasonable cpu-time. The FE data serve as a powerful assessment tool for analytical homogenization models. Newly developed and existing models for small and large strains are proposed and assessed, respectively, for both rigid particles and voids. These results fill the gap for large volume fractions of inclusions and serve as a reference for the homogenization of the microstructures of interest.