We consider a textile composite material reinforced by carbon fibers with 3D orthogonal braiding and a polymer matrix. Microstructural studies were carried out to find the mean values and variation coefficients for the parameters of the braid unit cell within the reinforcement cage. We have constructed an algorithm along with geometric models for cells and fragments of the composite structure, providing different descriptions for the parameters of the binder yarn. The micromechanics problem was solved by the local approximation method; the fields of structural stresses and strains were determined for different models of composite fragments. The fields were averaged to compute the composite's effective elastic properties compared to the experimental data.