We consider an approach to description of elastic properties of matrix polymer composite with hard particles of filler based on application of crystal model. At that, crystal lattices of cubic symmetry (ordinary cubic, cubic volume-centered, face-centered) and hexagonal symmetry are analyzed. When passing to isotropic polycrystal body, the methods of averaging are applied. These methods are based on the high invariants of tensors of modulus of elasticity (the Aleksandrov method), as well as on the Voigt method and the Reiss method. An advantage of the approach proposed is in creation of a background for description of matrix composites with hard particles of filler based on nonlocal, nonlinear theory of viscoelastic substances. Particularly, this method allows us to derive stiffness and dissipation matrices, which are included into the microscopic equation of particle motion.