MgH₂ is a promising compound for hydrogen storage. The theoretical hydrogen storage capacity of pure Mg is up to 7.6% of Hydrogen. In this thesis, the effects of alloying additions to MgH₂ will be investigated on the basis of improving dehydration thermodynamics. In this respect, the change in the formation energy of Mg_1-xM_xH₂ compound with respect to the choice of element M is going to be investigated via Local Density Approximation (LDA) to the Density Functional Theory (DFT). We will consider many possible alloying elements and structural modifications for these hydrides and study their equilibrium states. Additionally, charge density calculations will be carried out to understand the change of bond strength between H and Mg alloys resulting from the addition of selected alloying elements. The Density of States (DOS) will be examined and relation of these with the formation energies and bonding character will be presented.