We discuss the influence of geometry (both the shape and size) of dispersed inclusions on the properties of deformation and strength of composite materials with polymer matrixes in the case when the elastic and strength characteristics of the dispersed inclusions are higher by 2-3 orders as compared to the similar properties of a matrix. We construct “stress – strain” curves on the basis of analysis of representative volume of a material in such a way that the properties of the matrix and the inclusions and the characteristics of their interaction are taken into account explicitly. We perform such an analysis using a variant of the finite element method in collaboration with the procedure of step-by-step loading. As a result, we have an opportunity to study large deformations that run up to dozens and hundreds percents. It is pointed out that the shape of randomly oriented inclusions has no influence on the shape of the curve and consequently the size and the number of inclusions are of great importance in the case of constant degree of filling of a composition.