Using the group-theoretical approach of Blume and Orbach, a Hamiltonian is derived for interaction between coherent acoustic waves and rare-earth ions in cubic coordination. This Hamiltonian is found in partial agreement with the phenomenological spin-phonon Hamiltonian for effective spin 5=\ ions. Observations were made of the transmission of longitudinal and transverse 10-kMc/sec acoustic waves through rare-earth-doped CaF 2 as a function of an applied magnetic field. Magnetic-field-dependent attenuation of acoustic waves was observed for only two ions, Eu 2+ and Dy 3+ . In other cases only the upper limits of the acoustic absorption could be determined, and from these, lower limits of the direct-process relaxation time T\ were estimated. These lower limits were found approximately three orders of magnitude longer than the T\ values measured in CaF 2 at liquid-helium temperatures by the conventional pulse-saturation technique; an explanation of the discrepancy for some cases is suggested.146 268