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The structure and elastic properties of α-Zr and its hydrides were investigated by first-principle calculations and experimental methods. Considering all possible H-atom configurations, different phase models of hydrides were constructed. Results show that the stable structures of γ, δ and ε hydrides are P4₂/mmc, P4₂/nnm and I4/mmm, respectively. Calculation results suggest that ε hydride has the lowest formation enthalpy, and the phase transition sequence of γ → δ → ε is proposed. Compared with those of α-Zr, the c-axis lattice constants of hydrides become smaller, and the expansion volumes of γ, δ and ε unit cell are 12.1%, 14.8% and 17.9%, respectively. The calculated elastic modulus (E) of the three hydrides are lower than that of α-Zr, but their elastic anisotropy is higher than that of α-Zr. The elastic properties of α-Zr matrix and δ hydride were analyzed by nanoindentation experiment and the results show that E of the α-Zr matrix and δ hydride is 116.88 and 111.01 GPa, respectively. Therefore, the stress concentration is easy to occur on the hydride sides near the hydrides/matrix interface, so the hydrides are more likely to be the sources of crack and cause brittle fracture of zirconium alloys.