<p>The stiffness matrix for the composite material with spatially oriented unidirectional hollow fibers is constructed on the basis of the finite element moment scheme, which consists of the double approximation of the displacement fields and strain tensor components. This approach improves the convergence of numerical results and neutralizes such negative qualities of the traditional finite element method as the effect of “false” shear and failure to take into account the displacements of the finite element as an absolutely rigid whole. Direct consideration of the spatial angle of fiber reinforcement in the stiffness matrix makes it easier to set the initial data, reduce computational costs and errors in modeling problems by the finite element method (due to less restrictions on the development of discretization meshes). Using the proposed stiffness matrix, the axisymmetric problem for the hollow cylinder with different hollow fiber reinforcement schemes is solved. The comparison with analytical solutions for different fiber content in the composite and cavity in the fiber shows good convergence of numerical results to the exact solution.</p>