The reflection of elastic waves is customarily treated by assuming that the interface neither separates nor slips. This paper considers the reflection of SH waves that are strong enough to break friction between two solids which are pressed together, so that localized slip takes place. It is also assumed that the solids are sheared, which enhances slip in one direction and leads to a global sliding motion. The problem might at first appear as forbidding because of the mixed boundary conditions and the inequalities involved. It is discovered, however, that it can be solved in closed form for angles of incidence that avoid total reflection. The global sliding velocity, the sizes of the slip zones, and the rate at which mechanical energy is dissipated are displayed in terms of the independent variables involving the amplitude of the incident waves, and the applied pressure and shearing tractions.