The electronic structures of Mg_2X(X = Si,Ge,Sn) have been calculated by using generalized gradient approximation,various screened hybrid functionals,as well as Tran and Blaha’s modified Becke and Johnson exchange potential.It was found that the Tran and Blaha’s modified Becke and Johnson exchange potential provides a more realistic description of the electronic structures and the optical properties of Mg_2X(X = Si,Ge,Sn) than else exchange-correlation potential,and the theoretical gaps and dielectric functions of Mg_2X(X = Si,Ge,Sn)are quite compatible with the experimental data.The elastic properties of Mg_2X(X = Si,Ge,Sn) have also been studied in detail with the generalized gradient approximation,including bulk modulus,shear modulus,Young’s modulus,Poisson’s ratio,sound velocities,and Debye temperature.The phonon dispersions of Mg_2X(X = Si,Ge,Sn) have been calculated within the generalized gradient approximation,suggesting no structural instability,and the measurable phonon heat capacity as a function of the temperature has been also calculated. The electronic structures of Mg_2X (X = Si, Ge, Sn) have been calculated by using generalized gradient approximation, various screened hybrid functionals, as well as Tran and Blaha’s modified Becke and Johnson exchange potential. It was found that the Tran and Blaha’s modified Becke and Johnson exchange potential provide a more realistic description of the electronic structures and the optical properties of Mg_2X (X = Si, Ge, Sn) than else exchange-correlation potential, and the theoretical gaps and dielectric functions of Mg_2X (X = Si, Ge, Sn) are quite compatible with the experimental data. The elastic properties of Mg_2X (X = Si, Ge, Sn) have also been studied in detail with the generalized gradient approximation, including bulk modulus, shear modulus, Young’s modulus, Poisson’s ratio , sound velocities, and Debye temperature. The phonon dispersions of Mg_2X (X = Si, Ge, Sn) have been calculated within the generalized gradient approximation, suggesting no structural instability, and the measurable phonon heat c apacity as a function of the temperature has been calculated also