High sedimentation rates on the subaqueous delta of the Mississippi River create localized sediment instabilities that result in downslope movement through well-defined chutes or gullies. A simplified kinematic wave equation model that neglects second-order effects such as diffusion treats the failure mechanism as a sedimentation and slope oversteepening process and sediment motion as a propagating kinematic wave. The model allows estimation of sedimentation rates necessary to initiate slope failures for a range of observed depths of basal shear planes. Model results indicate that slope oversteepening is a viable failure mechanism and a thin surface sediment layer may be moving downslope in a slow, continuous motion.