Young’s modulusEand the modulus of rigidityGof zirconium hydridesZrHx(0.9⩽x⩽1.65)at 941 and 1001 K have been obtained as a function of hydrogen concentrationcby measuring resonance frequencies for bending and torsion vibrations of a polycrystalline wire. Ascincreases, observedEandGincrease in the bcc &bgr; phase, slightly increase linearly in the&bgr;+&dgr;phase, and then decrease in the fcc &dgr; phase. On the basis of a phenomenological free energy in terms of strain components taking account of space group symmetry, two types of Landau expansion of the free energies for the &bgr; phase in terms of the strain components which play an important role in the structural phase transition between the &bgr; and the &dgr; phases are examined. The observedEandGare assumed to be the same as the second-order coefficients of the free energy for the Bain distortions, which occur at the structural phase transition. The dependence of the third-order coefficients oncpermits the expanded free energies to describe the fact that the &bgr; phase is more stable than the &dgr; phase at lowc.©1997 American Institute of Physics.