Elasticity tensor components, Cij, the crystallographic dependence of Poisson’s ratio, the phase stability, and vibrational spectra are computed for nonmagnetic and magnetic CeMg (1:1 Ce:Mg) structures using density functional theory. Results from both the generalized gradient approximation (GGA), and the GGA+U , based upon an effective on-site Coulomb potential, Ueff, are investigated. The GGA low energy structure, with wavevector along [110], disagrees with experiment, while the [100] structure from experiment is predicted as the 0 K structure in the GGA+U . Accurate estimation of the 20 K Néel temperature can only be achieved with small Ueff, which suggests that CeMg is not a strongly correlated system. For all CeMg structures investigated, we find C₁₁≈C₄₄; this is consistent with the near equivalency of transverse and longitudinal sound speeds. The origin of this behavior is the negative stretching force constants for the interaction between the second- and third-nearest-neighbor Mg and Ce ions, respectively. Results are compared with neutron scattering experiments at 30 and 110 K.