We examine an original approach to modelling the mechanical properties of polymer composites with hard filler particles and an elastomeric matrix, based on the use of a multiparticle ordered physical model. Using the hypothesis of the analogy between the composite material and a crystal, we are able to apply the well developed mathematical apparatus of the microscopic theory of crystals to describe the mechanical properties and the physical laws governing the behavior of polymer-matrix composites. In the present article, which is the first part of the work, we examine the elastic approximation.