  We consider the stability of a system of equations which are a singular
perturbation of the incompressible rigid-plastic flow equations used to model
granular flow. A linear stability analysis shows that solutions of these
equations are unstable, in general, and that these instabilities may lead to
ill-posedness. However, the analysis suggests that these equations are more
regular, in a certain sense, than the unperturbed incompressible rigid-plastic
flow equations. Numerical solutions are presented which illustrate the growth
of instabilities and the development of shear-bands in the flows.
