The paper considers seven types of lattice structures of different topologies, which are periodic unit cells of metamaterials to be manufactured by additive technologies. We carried out finite-element analysis of lattice structures with varying thicknesses of elementary beams comprising the cells and varying initial symmetric shapes. The effective elastic properties of metamaterials as continuous media were calculated by the method of direct numerical homogenization with periodic boundary conditions. The dependences between elastic properties and characteristic parameters determining the topology of cells were established. Some types of lattices were found to exhibit auxetic properties in a certain range of topological parameters.