Composite lattice plates and shells consisting of system of unidirectional ribs and fabricated by filament winding are characterized with high weight efficiency and are used in aerospace structures. The paper concerns with a possible approach to obtain the efficient stiffness characteristics of lattice structures with a dense and periodic system of ribs. In case the lattice structure is formed by ribs forming periodic system of elementary cells translating which we can describe the whole structure, the real structure can be simulated with a smooth structure characterized by efficient stiffness characteristics. This simulation is of a special interest for the problems of design of lattice structures. The approach proposed in the paper is based on the Helmholtz theorem which allows us to link the displacements of the adjacent points in a solid. Applying this approach, the strain energy can be expressed first in terms of the cell energy and then through the displacements of the end cross-sections of the ribs in the cell and finally through the displacements and strains in the solid element simulating the cell. The strain energy of the lattice structure can be then obtained summing up the energies of the cells. Constitutive equations including efficient stiffness coefficients are derived with the aid of the Castigliano theorem. These equations allow us to determine the forces and the moments acting in the ribs. Lattice structures formed by several systems of ribs with different orientations are considered and analyzed.