First-principles calculations have been carried out to investigate the effects of alloying elements (Zn, Li, Y and Sc) on the electronic structure, elastic and thermal properties of Mg solid solution. The calculated cohesive energies show that Mg-Sc has the highest structural stability. The calculations of the densities of states (DOS) and electronic charge density difference indicate that Mg-Y (Sc) alloys have very strong covalent bonding due to a very strong Mg p-Y(Sc) d hybridization. The bulk modulus B, shear modulus G, Young\'s modulus E and Poisson ratio v are derived using Voigt-Reuss-Hill (VRH) approximation. The results show that all the alloys can exhibit ductile properties at 2.77 at％ R, and Mg-Zn(Li) alloys have the better ductility and plasticity. In the end, the Debye temperature and isochoric heat capacity are also calculated and discussed.