A new polymer composite material composed of a fibre reinforced filler and two types of matrices: thermosetting (epoxy) and elastomeric (organosilicon) is introduced. The main purpose of the elastomeric matrix is stress relaxation and slowdown and prevention of crack growth in the composite material under dynamic loads, including bending and delamination. In this study, a finite element model of such composite is developed and its stress-strain state is calculated depending on the elastic characteristics of the elastomer. It was established that the addition of an elastomeric matrix in the composite allows to stop the crack growth, and significantly increase the durability of such materials.