Structural stabilities, elastic properties and electronic structures of Mg17Al12, Al2Y and Al2Ca phases have been determined by Castep and Dmol program based on the density functional theory. The calculated heats of formation and cohesive energies show that Al2Y has the strongest alloying ability as well as the highest structural stability. The calculations of thermodynamic properties display that the Gibbs free energy of Al2Y is always the smallest and it has the highest stability within 298~573 K. The next is Al2Ca, and the last one is Mg17Al12. Y and Ca addition to the Mg-Al alloys can improve the heat resistance. The calculated elastic constants reveal that Mg17Al12, Al2Y and Al2Ca are all brittle, and among the three phases Mg17Al12 is a phase with the best plasticity. The results of elastic constant calculation predict that Al2Y has the highest melting temperature and the best structural stability. The calculations of the density of states (DOS) and Mulliken electronic populations indicate that the highest structural stability of Al2Y attributes to more covalent bonds below Fermi level compared with those of Mg17Al12 and Al2Ca phases.