First-principles calculation reveals that the ZrHx phases (x = 1, 1.25, 1.5, 1.75, and 2) with the cubic fluorite-type (fcc, delta phase) and face-centered-tetragonal (fct: epsilon phase, c/a < 1; gamma phase, c/a > 1) structures are all energetically favorable with negative heats of formation of -30 to -56 kJ/(mol H) and very small structural energy differences, while mechanical stability plays a more important role in determining the existence of various ZrHx phases. Calculation also shows that the intrinsic composition range of the delta -> epsilon transition of ZrHx phases is x >= 1.5, and that the fundamental mechanism of this transition is mechanical unstableness of the delta phase which will spontaneously transform into epsilon phase by means of the {110}< 110 > shear. Moreover, electronic structures show that the co-function of van Hove singularities and degenerate bands along several directions brings about the high level of density of states at or near the Fermi level and fundamentally induces the mechanical unstableness of the delta phase. Copyright (C) 2012, Hydrogen Energy Publications, LLC. Published by Elsevier Ltd. All rights reserved.