A numerical model of river morphology for meander bends with erodible cohesive banks is herein developed and tested. The new model has three key features. First, it couples a two-dimensional depth-averaged model of flow and bed topography with a mechanistic model of bank erosion. Second, it simulates the deposition of failed bank material debris at and its subsequent removal from the toe of the bank. Finally, the governing conservation equations are implemented in a moving boundary fitted coordinate system that can be both curvilinear and nonorthogonal. This simplifies grid generation in curved channels that experience bank deformation, allowing complex planform shapes associated with irregular natural channels to be simulated. Model performance is assessed using data from two flume experiments and a natural river channel. Results are encouraging, but the model underpredicts the scour depth in pools adjacent to the outer bank and, consequently, underpredicts bank migration rates.