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The structural properties, heat of formations, elastic properties, and electronic structures of Ni-Al and Ca-X（X=Si,Ge,Sn,Pb,Zn） intermetallic compounds were analyzed in detail by using density functional theory.For Ni-Al intermetallic compounds, higher calculated absolute values of heats of formation indicate a very strong chemical interaction between Al and Ni. According to the computational single crystal elastic constants, all the Al-Ni intermetallic compounds considered are mechanically stable. The polycrystalline elastic modulus and Poisson’s ratio were deduced by using Voigt, Reuss, and Hill （VRH） approximations, and the calculated ratio of shear modulus to bulk modulus indicated that AlNi, Al3Ni, AlNi3 and Al3Ni5 compounds are ductile materials, but Al4Ni3 and Al3Ni2 are brittle materials. With increasing Ni concentration, the bulk modulus of Al-Ni intermetallic compounds increases in a linear manner. The electronic energy band structures confirm that all Al-Ni intermetallic compounds are conductors.We also study the properties of Ca-X（X=Si,Ge,Sn,Pb,Zn） intermetallic compounds. According to the computational single crystal elastic constants, except Ca36Sn23, CaZn3, all the other Ca-X intermetallic compounds considered are mechanically stable. The results of polycrystalline elastic properties indicate that Ca2Sn, Ca7Sn6, CaSn3, Ca2Pb, CaPb3, Ca3Zn, Ca5Zn3, CaZn, CaZn11 are ductile materials, and the others are brittle materials. Higher calculated absolute values of heats of formation indicate a very strong chemical interaction between Ca and Si, Ge, Sn, Pb due to the research of the heat of formation. But the heats of formation for Ca-Zn intermetallic compounds are obviously smaller than Ca-X （X=Si,Ge,Sn,Pb）. Finally the electronic energy band structures are studied. According to the result, Ca2Si, Ca2Ge, Ca2Sn, Ca2Pb are direct-gap semiconductor. And their band gaps are 0.324eV, 0.265eV, 0.06eV and 0.07eV, respectively. Ca3Si4 is indirect band gap semiconductor and its band gap is 0.598eV. All the other compounds are conductors.
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