Hydrogen induced embrittlement and associated cracking effects in Zirconium alloys impose a serious problem, for example, within the nuclear industry where these materials are used in a range of applications, including fuel claddings. To get a fuller understanding of the hydrogen diffusion, hydride formation and phase transformations taking place at conditions of external stress and at elevated temperature it is crucial to augment experimental measurements with multi-level modelling. It is, for example, possible to simulate hydride phase-transformation trough phase-field calculations[1]. In order to get accurate results from these calculations, however, it is important to have basic physical information, such as interfacial energies and elastic constants. The latter were obtained completely from first principle calculations of density functional theory. In pure zirconium, at low hydrogen concentrations and at low temperatures, hydrogen atoms are dissolved into the matrix and preferentially occupy tetrahedral sites within the thermodynamically stable aZr hexagonal closed packed unit cell. At higher concentrations the various face centred cubic and tetragonal hydride phases start to form. Using the plane-wave code DACAPO, within the generalized gradient approximation, the lattice parameters and the ionic positions of bulk aZr, dZrHx and gZrHx were relaxed with respect to total energies. The formation energies as well as bulk moduli were then obtained by fitting total energies as a function of lattice parameters with a 3rd or 4th order polynomial. By comparing the present results with previous calculations and experiments it was possible to validate the methods for further use. The results, thus, comprise a foundation and serves to verify methods and codes. The next step is to compute more complex properties such as surface free energies, or interfacial energies, of bi-phase Zr-H systems, so that the full multiscale model can be implemented. 1. V. Vaithyanathan et al., Acta Materialia 52 (2004) p. 2973