In this paper, the structural, elastic and phonon properties of Ti 3 Al and Y 3 Al in L1 2( Cu 3 Al ) phase are studied by performing first-principles calculations within the generalized gradient approximation. The calculated lattice constants, static bulk moduli, first-order pressure derivative of bulk moduli and elastic constants for both compounds are reported. The phonon dispersion curves along several high-symmetry lines at the Brillouin zone, together with the corresponding phonon density of states, are determined using the first-principles linear-response approach of the density functional perturbation theory. Temperature variations of specific heat in the range of 0–500 K are obtained using the quasi-harmonic model.