Results of computational finite-element simulation are presented for processes of microdestruction of multidimensional reinforced composite materials. The simulation is based on applying the asymptotic homogenization method and finite-element approximate solving the local problems over a periodicity cell. As a criterion of the matrix strength, the modified Pisarenko-Lebedev model has been used, and as a criterion of the reinforcing fibers’ strength, the model of damage of a monofibers’ bundle has been applied. It was shown that the model allows us to analyze different scenarios of composites’ microdestruction under changing loads for different combinations of elastic-strength properties of a matrix and fibers. Computed results are presented, which show possibilities of the developed model for numerical investigation of microdestruction processes of 3D orthogonally reinforced composites. And comparison of the computed results with data of experiments has been conducted.