Detailed measurements are presented of ultrasonic wave velocity and attenuation of the orthorhombic superconducting and the tetragonal, non-superconducting forms of GdBa₂Cu₃O_7-x. The orthorhombic state data display a sharp elastic transition at about 240 K which is absent from that of the tetragonal state; however, X-ray diffraction measurements show no evidence of a structural phase transition. The lattice thermal expansion is found to be fairly isotropic. The elastic response in the superconducting state is found to be dominated by conventional anharmonic and anelastic phenomena: no effects that can be specifically attributed to the formation of the superconducting state have been detected. The ultrasonic velocity and attenuation data are explained by the presence in the tetragonal state of one and in the orthorhombic state of two thermally activated anelastic relaxation mechanisms which are attributed to various oxygen vacancy hopping processes.