Precipitation of brittle zirconium hydrides deteriorate the fracture toughness of the fuel cladding tubes of light water reactor. Although the hydride embrittlement has been studied extensively, little is known about physical properties of the hydride due to the experimental difficulties. In the present study, to elucidate relationship between mechanical properties and microstructure, two δ-phase zirconium hydrides and one ε-phase zirconium hydride were carefully fabricated considering volume changes at the metal-to-hydride transformation. The δ-hydride that was fabricated from α-zirconium exhibits numerous inner cracks due to the large volume change. Analyses of the neutron diffraction pattern and electron backscatter diffraction (EBSD) data show that the sample displays significant stacking faults in the {111} plane and in the pseudo-layered microstructure. On the other hand, the δ-hydride sample fabricated from β-zirconium at a higher temperature displays equiaxed grains and no cracks. The strong crystal orientation dependence of mechanical properties were confirmed by indentation test and EBSD observation. The δ-hydride hydrogenated from α-zirconium displays a lower Young's modulus than that prepared from β-zirconium. The difference is attributed to stacking faults within the {111} plane, for which the Young's modulus exhibits the highest value in the perpendicular direction. The strong influence of the crystal orientation and dislocation density on the mechanical properties should be considered when evaluating hydride precipitates in nuclear fuel cladding.