We performe first-principles density functional theory calculations to investigate the stability and mechanical properties of various Hf Hx(0 ≤ x ≤ 1) phases. For pure Hf phases, the calculated results show that the HCP and FCC phases are mechanically stable, while the BCC phase is unstable at 0 K. Also, as for various Hf Hx phases, we find that H location and concentration could have a significant effect on their stability and mechanical properties. When 0 ≤ x ≤ 0.25, the HCP phases with H at(tetrahedral) T sites are energetically most stable among various phases. The FCC and BCC phases with H at T sites turn to be relatively more favorable than the HCP phase when H concentration is higher than 0.25. Furthermore, our calculated results indicate that the H solution in Hf can largely affect their mechanical properties such as the bulk moduli(B) and shear moduli(G). For pure Hf phases, the calculated results show that the HCP and FCC phases are mechanically stable, while the BCC phase is unstable at 0 K. Also, as for various Hf Hx phases, we find that H concentration and concentration could have a significant effect on their stability and mechanical properties. When 0 ≤ x ≤ 0.25, the HCP phases with H at ( Thehedral and T site turn to be relatively more favorable than the HCP phase when H concentration is higher than 0.25. Further, our calculated results indicate that the H solution in Hf can substantially affect their mechanical properties such as the bulk moduli (B) and shear moduli (G).