The second and third order elastic constants of seven simple metals (Li, Na, K, Eb, Cs, Al and Pb) are calculated using the one-parameter Heine-Abarenkov model potential with the Hubbard-Sham dielectric function. The two adjustable parameters are determined from the experimental data of the elastic constant C44 and the lattice constant of the crystal at 0 K and zero pressure. The calculated results are in comparatively good agreement with the experiments or the theoretical calculations of other authors. Especially for Al, the present results of the third order elastic constants are closer to the experimental data than those found in the literatures.