The paper presents a numerical simulation of the contact interaction of fibrous polymer composite materials in a finite element ANSYS package and studies the friction coefficients for cells with wear of 0%, 25%, 50% and 75%. To predict the coefficient of friction of composites it was proposed to use the method of mechanics of composite materials – the method of local approximation. With the help of numerical simulation, the fields of distribution of normal stresses and contact stresses in the contact zone were obtained and the corresponding conclusions were drawn.