[en] Hf hydride is proposed to be used as neutron control materials for fast reactors. The electronic, mechanical and thermal properties of its three phases: δ′-HfH_1.5, δ-HfH_1.75, ε-HfH₂, are investigated. Their relative stabilities at 0 K by our calculation are consistent with the explanation of Jahn–Teller mechanism. The mechanical properties like elastic constants are calculated and agree well with the experiments. At finite temperatures, in addition to the direct method for phonon calculation, electronic free energy is also calculated in order to investigate the thermal expansion and bulk moduli of three phases. Hf–H system has an increasing relationship in bulk moduli with respect to the H concentration before about 360 K, after which ε-HfH₂ seems to decrease more quickly in the softness of the structure than δ-HfH_1.75 as the temperature increases. The relation between heat capacity and Hf and H atoms vibration is discussed