The propagation of plane waves in a piezoelectric medium has been studied. A simultaneous solution of Maxwell's field equations and Newton's law of force gives the necessary conditions for wave propagation in the infinite medium. By piezoelectric coupling, every electromagnetic wave has associated with it an elastic wave. Nonpiezoelectric crystals are, at best, birefringent electromagnetically and trirefringent acoustically. In piezoelectric media, the electromagnetic and elastic modes are coupled, thus giving five phase velocities for both the electromagnetic and acoustic waves. These media are therefore electromagnetically and acoustically pentrefringent. The slower electromagnetic waves are the field variations accompanying the elastic waves, while the fast elastic waves are the mechanical deformations accompanying the electromagnetic wave.The displacement in the elastic wave will differ in phase by ninety degrees from the electromagnetic wave, its amplitude being proportional to the electric field strength and inversely proportional to the frequency of vibration. The flux of energy will, in general, be in directions different from that of phase propagation. The generalized Poynting vector will be the sum of two vectors representing separately the flux of electromagnetic energy and the flux of elastic energy.Analysis was made of propagation in a particular direction in sphalerite. The orientation of the vectors involved has been calculated for the fast and slow modes of vibration.A study of specific boundary value problems gives interesting results. The piezoelectric effect gives a contribution to the reflection of electromagnetic waves at an interface. This results in a small correction to be applied to the familiar expressions for the reflection coefficients. This correction might be used to determine piezoelectric constants, providing it is possible to measure accurately the reflection coefficients and other constants involved.Slabs of piezoelectric media may be set into vibration by an incident electromagnetic wave. At particular frequencies the crystal may be set into resonance. At resonance for the elastic wave there is almost perfect reflection of the incident electromagnetic wave. It should be possible to detect these resonances by absorption measurements.The piezoelectric slab, if set into resonance by an acoustic wave, emits a weak electromagnetic signal.