Lattice parameters, electronic and vibrational energies, enthalpies of formation at 0 and 298 K, the elasticity tensor components, Cij, polycrystalline bulk, shear and Young’s moduli based on the Hill criteria were computed for LaMg, LaMg₂, LaMg₃, La₅Mg₄₁, La₂Mg₁₇, and LaMg₁₂. The quasiharmonic approximation was used to compute the linear thermal expansion tensor, aij(T), and the constant pressure heat capacity, Cp(T). Elastic anisotropy was analyzed in terms of the Young’s moduli dependence on crystallographic direction. Results were compared with available experimental data and discussed in terms of the applications of materials from the La-Mg system.