Excessive river erosion and sedimentation threatens critical infrastructure, degrades aquatic habitat, and impairs water quality. Tools for predicting the magnitude of erosion, sedimentation, and channel evolution processes are needed for effective mitigation and management. We present a new numerical model that simulates coupled river bed and bank erosion at the watershed scale. The model uses modified versions of Bagnold’s sediment transport equation to simulate bed erosion and aggradation, as well as a simplified Bank Stability and Toe Erosion Model (BSTEM) to simulate bank erosion processes. The model is mechanistic and intermediate complexity, accounting for the dominant channel evolution processes while limiting data requirements. We apply the model to a generic test case of channel network response following a disturbance and the results match physical understanding of channel evolution. The model was also tested on two field data sets: below Parker Dam on the lower Colorado River and the North Fork Toutle River (NFTR) which responded dramatically to the 1980 eruption of Mount St. Helens. It accurately predicts observed channel incision and bed material coarsening on the Colorado River, as well as observations for the upstream 18 km of the NFTR watershed. The model does not include algorithms for extensive lateral migration and avulsions and therefore did not perform well in the lower NFTR where the channel migrated across a wide valley bottom. REM is parsimonious and useful for simulating network scale channel change in single thread systems responding to disturbance.