The Frank-Oseen elastic constants K-11, K-22 and K-33 as well as the surface constants K-13 and K-24 have been calculated for Gay-Berne nematic liquid crystal with anisotropy parameters k = 3 and k’ = 5. In deriving the elastic constants a direct correlation func tion approach of Poniewierski and Stecki(1) in a version proposed by Lipkin et al.(5) was choosen. The final formulas have been expressed in terms of the orientational order parameters and of the angular coefficients of the direct correlation function of an unoriented nematic. The latter have been determined exactly from the molecular dynamics simulations in the NVT ensemble. Results for the surface elastic constants, qualitatively different than those obtained from all previous treatments, clearly show that the surface deformations are strongly sensitive to details of the direct correlation function. Obtained values of surface elastic constants are partly negative and an order of magnitude smaller than bulk elastic constants.