In our earlier work [Phys. Rev. E, 82, 041701 (2010)], the bulk elastic constants were calculated using Poniewierski-Stecki expressions and the new direct correlation function. We calculated the bulk elastic constants, K-11, K-22 and K-33 of Gay-Berne nematic liquid crystals at constant temperature and density using the expressions proposed by Stelzer and co-workers [J. Chem. Phys. 103, 3098 (1995)]. The angular coefficients of the direct correlation function, which enter the final equations, have been determined using the new direct correlation and pair distribution functions. By study of the model at a fixed temperature over a wide range of densities for molecular elongation, k = 3, the detailed information is provided on the elastic behavior of the Gay-Berne nematic. The results of our calculations are qualitatively in agreement with the molecular dynamic simulation results.