Zirconium alloys are considered to be the main structural materials within the cores of nuclear reactors. The need for a better efficiency of the nuclear industry is a driving force for the improvement of the properties of the alloys used, i.e.corrosion resistance and mechanical behavior. Although zircaloys are the best choice for fuel cladding and pressure tubes in nuclear reactors, they have several drawbacks. Zirconium has a tendency for hydrogen pick-up. At low temperatures zirconium –phase has low solubility of hydrogen which gives rise to any excess of hydrogen get precipitated as zirconium hydride. This leads to serious consequences such as hydrogen embrittlement. Understanding the basic nature and mechanisms of hydride formation, transformation and exact structure is therefore critical for the safety of nuclear reactors. The purpose of this project is to investigate a new phase for zirconium hydride (Zr2H) named zeta ( ) which has been recently identified and characterized in other previous researches. This phase has a hexagonal lattice and belongs to the trigonal crystal system with space group P3 m1 that is fully coherent with the –Zr matrix. Other structures have also been studied in order to assess the most convincing structure that represents this new phase. This has been done through implementing DFT-calculations on Zr2H using the software Quantum Espresso (QE). Formation energies of seven candidate hydride structures have been calculated and they are found out to be in agreement with other results considering the minimum energy.