We present a phenomenological-type applied theory of composite materials. This theory allows us to perform a micro-mechanical analysis of composite materials with small volume content of reinforcing fibers in the case of large deformations of structural components. Macroscopic stresses of composites are determined in the form of a sum of macroscopic stresses in the reinforcing fibers and macroscopic stresses in the matrix; at that, the macroscopic stresses in the matrix depend on the macroscopic deformation specified in advance. Based on the comparison of the results obtained by the applied theory proposed and the rigorous skeleton theory, we determine the limiting values of a volume content of reinforcing fibers corresponding to the limit of applicability of the applied theory.