In the paper, an elastic-plastic medium is investigated from an inhomogeneous solid material consisting of two components: reinforcing elements and a matrix (or binder), which ensures the joint operation of reinforcing elements. Based on the asymptotic methods of calculating composite materials, taking into account the internal structure, the effective mechanical parameters of the fiber composite are determined. This makes it possible to bring the inhomogeneous medium to a uniform, with different mechanical parameters along the isotropy and isotropy planes. To solve the problem of physically nonlinear deformation of fibrous composites, a simplified theory of small elastic-plastic deformations for a transversely isotropic medium is proposed, proposed by prof. B.Е. Pobedrya. This allows us to apply the theory of small elastic-plastic deformations for solving applied problems. The solution of the elastic-plastic problem is performed on the basis of the iterative process of the method of elastic solutions of AA Ilyushin and FEM. It is known that the presence of a stress concentrator in the constructions leads to a significant distortion of the stress distribution pattern. In the vicinity of the hole there is an increased tension. On the basis of the developed computer model for calculating the physically nonlinear deformation of fibrous composite materials with stress concentrators, a computer experiment was carried out. The stress-strain state of plates weakened by a through hole in the form of a flattened elliptic cylinder and a horizontal rectilinear crack is studied. The influence of the shape of the holes on the formation of plastic deformations in structures made of fibrous structures is studied. The location of the zones with the maximum tangential stresses, which can lead to fiber detachment from the matrix, is determined. The process of stress reduction is studied by changing the shape of the contour with a minimally distorted stress state. The effect of additional round holes on the stressed state of the plate was studied. It is established that if in the constructive relation at a distance of one diameter from the first hole it is permissible to establish a second one, it causes unloading of the plates in the vicinity of the stress concentrators. Thus, by means of structural changes, an improvement in the distribution of stresses and, as a result, an increase in the strength of the structure is achieved.