In this paper it is demonstrated that relatively slow, quasi-static slippage on a fault that separates two half spaces of different elastic constants can become unstable if the slippage is governed by Amontons-Coulomb friction law (the shear stress across a fault required for slipping motion is proportional to the normal compressive stress across the fault). If the two half spaces have identical properties, unstable slipage is not possible under this friction law. The unstable slippage that is investigated in this paper is a consequence of the existence of a short-range normal traction stress that gliding edge dislocations produce across an interface between two half spaces of different elastic constants. This normal traction stress does not exist if the two half spaces have identical properties. (Recent work of Dundurs and Comninou and their co-workers has revealed the importance of the short-range traction stress components to crack problems.)