Laboratory deformation studies of metals and some oxides indicate that these solids are easily deformed while undergoing a phase transformation. This superplastic effect, if it occurs for mantle silicates, may result in an instability of mantle flow. The instability is illustrated by considering a sheared layer of viscous fluid containing a phase transition. With a simple idealization of the phase transition weakening effect, an oscillatory fluid motion which cycles material through the phase transition is shown to reduce the rate of viscous dissipation associated with shearing the fluid layer. Some possible consequences for mantle flow include the partial decoupling of mantle layers at phase transitions and short wavelength free air gravity anomalies due to induced normal stress variations at the base of the lithosphere.