The deformation behaviors of second phases are important in understanding the mechanical properties of Mg alloys. In the present work, the elastic constants of magnesium based binary compounds have been predicted from first principles calculations using the stress strain method . The Mg-X systems that have been investigated in the present work include Mg-As, -Ba, -Ca, - Cd, -Cu, -Dy, -Ga, -Ge, -La, -Ni, -Pb, -Sb, -Si, -Sn and -Y. A comparative study between the results obtained in the current work and the available experimental data has been made. The accuracy in the calculated data sets off a landmark to use the same for any future work incorporating the design of Mg based alloys.