ABSTRACTThis is a survey of recent theoretical work on shear flow instabilities of dry granular media in the Bagnold or “grain-inertia” régime. Attention is devoted to steady homogeneous unbounded simple shear, with the goal of identifying material (constitutive) instabilities arising from the coupling of stress to granular concentration and temperature fields. Such instabilities, the dissipative analogs of thermodynamic phase transitions, are familiar in numerous branches of the mechanics of materials.The current interest is motivated in part by the “dissipative clustering” found in various particle-dynamics (“DEM”) simulations of granular systems. Since particle clustering may invalidate standard gas kinetic theory, it is pertinent to ask whether hydrodynamic models based on such theories may themselves exhibit clustering instability.The present article is based largely on a recent review (Goddard and Alam 1999), which provides a unified linear-stability treatment for rapid granular flow, as well for slow flow of mobile particles immersed in viscous liquids. The analysis is based on a “short-memory” response of various fluxes to perturbations on steady uniform states, a feature characteristic of the most popular constitutive models for granular flow. In the absence of gravity, previous theoretical analyses reveal transverse “layering” and spanwise “corrugations” as possible forms of material instability (Alam and Nott 1998)Based on current theoretical findings, further work is recommended, including the exploration of the effects of gravity and of stress relaxation, both of which are likely to be important in real granular flows.