Recent plate impact experiments have been interpreted as indicating the existence of “failure waves” during the compression of glass by impact at sufficiently high velocities. In experiments on soda-lime glass, Brar et al. (1991) reported the propagation of a wave across which the shearing strength dropped sharply from 2 GPa to 1 GPa, and the spall strength dropped from 3 GPa to zero. Such a drop in spall strength has also been reported by Raiser et al. (1993) in an aluminosilicate glass. Kanel et al. (1993) interpreted a small jump in the rear surface particle velocity in experiments on K19 glass as the reflection of a recompression wave from a wavefront propagating at approximately the speed reported for “failure waves”. In this paper, such “failure waves” are interpreted within the context of nonlinear wave theory. In this theory the “failure wave” corresponds to a propagating phase boundary—called a transformation shock. The theory is analogous to the theory of liquifaction shocks in fluids.