Density Functional Theory computations are useful tools in the study of materials behaviour in presence of Hydrogen, and can be a valid help in the analysis of Hydrogen production processes and storage. In the present paper this technique is applied to Tantalum, a possible material for the realization of membranes for Hydrogen purification, resistant to highly corrosive environment (e.g. in the separation step in the Sulphur-Iodine process). A DFT study of the Tantalum lattice with interstitial Hydrogen at different concentrations is presented, with: a discussion on the preferential interstitial sites; a study of the displacements of Ta atoms caused by the Hydrogen presence, and of the interaction between two Hydrogens in the lattice; the calculation of the heat of solution and of the enlargement of the lattice at different Hydrogen concentrations; and, finally, the dependence of two elastic constants on the Hydrogen concentration, an important aspect in the study of the structural resistance of the material. Copyright (C) 2011, Hydrogen Energy Publications, LLC. Published by Elsevier Ltd. All rights reserved.