The effects of Y and Zn atoms on elastic properties of Mg solid solution are investigated by first-principles calculations based on density function theory. Five supercell models (Mg96, Mg95Y1, Mg94Y2, Mg95Zn1 and Mg94Zn2) are adopted to simulate the variation of solute atoms content. Structural optimization is performed firstly, and then the five independent elastic constants of Mg solid solution are calculated. The bulk modulus B, shear modulus G, Young's modulus E and Poisson ratio ν are also derived by Voigt–Reuss–Hill (VRH) approximation, indicating a strong dependence of the elastic modulus on concentration of the solute atoms. Using the bulk modulus/shear modulus ratio (B/G), the change in the ductility of Mg solid solution with the solute atom content is further studied. In the end, the electronic density of states (DOS) is calculated and discussed.