Molecular dynamics (MD) simulations and Brillouin light scattering (BLS) spectroscopy experiments have been carried to study the structure of sodium silicate glasses (SiO2)((100-x))(Na2O)x, where X ranges from 0 to 45 at room temperature. The MD-obtained glass structures have been subjected to energy minimization at zero temperature to extract the elastic constants also obtained by BLS spectroscopy. The structures obtained are in good agreement with the structural experimental data realized by different techniques. The simulations show that the values of the elastic constants as a function of X (i.e., Na2O mol %) agree well with those measured by BLS spectroscopy. The variations of elastic constants C-11 and C-44 as a function of Na2O mol % are discussed and correlated to structural results and potential energies of oxygen atoms.