The calculated transmission of microwave power at GHz frequencies through Terfenol-D (Tb0.27Dy0.73Fe2) is strongly influenced by the enormous magnetostriction parameter of this material. For conditions satisfying ferromagnetic resonance there is a peak in the transmission corresponding to sound and spin waves transporting energy through a slab-shaped sample. The magnetostriction mixes the character of these waves; the calculated transmission also depends on the exchange stiffness parameter, the elastic constants, and the radio-frequency magnetic properties. With thin (<40 μm) samples for which the static magnetization is along the magnetically soft (111) direction the calculated transmission peak is augmented by a fringe pattern with more than 20 secondary peaks. This arises from interference between spin and sound waves. For the configuration with the static magnetization oriented along the magnetically hard (100) direction the fringe pattern is absent. In this configuration the spin wave is a soft mode and the sample should develop a static distortion of the magnetization and lattice. The periodicity of this static distortion is tunable with an external magnetic field, although lattice imperfections may introduce hysteresis by pinning the distortion.