We studied the thermodynamics of interstitial Mg:H solid solutions by means of ab-initio electronic structure calculations. Soft pseudopotentials (Troullier-Martins) with non linear core correction and Perdew-Burke-Ernzerhof GGA exchange-correlation functional were employed, in the framework of a DFT plane-wave scheme. We inserted increasing concentrations of interstitial H atoms in the hcp Mg lattice, in both tetrahedral and octahedral positions. We calculated the heat of solution and the volume variation as a function of H concentration. Although the difference in Gibbs free energy is positive at any H concentration above 10−6 at.%, our results show that the enthalpic contribution is negative at any H concentration, therefore locally favouring H clustering. This reflects the existence of a driving force for the subsequent formation of the hydride. The volume deformation was characterized, finding that octahedreal interstitials have a minor effect, while tetrahedral interstitial can induce very large local expansion.