A direct method is proposed for solution of large systems of linear algebraic equations appearing in the application of the method of finite elements. The method is based on dividing the given structure into a system of deeply embedded substructures which are not intersecting. The dividing is carried out automatically by the method of embedded intersections. Efficiency of the method is established by comparison with the method of conjugated gradients with a spectral-equivalent operator of the inco mplete Cholesky factorization type and the traditional profile method using the example of a circular cylindrical shell stiffened by high ribs.