The structural stability, electronic structures and elastic properties of Mg17Al12, Mg2Sn and Al2Y phases in Mg-Al-Sn-Y alloy have been investigated by CASTEP program based on the density functional theory. The calculated results of heats of formation and cohesive energies show that Al2Y phase has the strongest alloying ability and structural stability. The structural stability mechanism and the brittle behavior were obtained from the electronic structure of these three intermetallic compounds. The three independent crystal elastic constants of Mg17Al12, Mg2Sn and Al2Y phases were calculated; bulk modulus, shear modulus, Young’s modulus, and Poisson’s ratio were predicted. Further analysis shows that Mg17Al12, Mg2Sn and Al2Y phases are all brittle phases, and Al2Y are the brittlest and stiffest.