The application of many existing numerical models of river channel morphology is limited by their inability to account for bank erosion and changing channel width through time. In this research, a physically-based numerical model which simulates the evolution of channel morphology, including channel width, through time has been developed and tested. Predictions of channel evolution are obtained by solving deterministically the governing equations of flow resistance, flow, sediment transport, bank stability and conservation of sediment mass. The model is applicable to relatively straight, sand-bed streams with cohesive bank materials. In the channel evolution model, a method is used to solve the shallow water flow equations, and to account for lateral shear stresses which significantly influence the flow in the near bank zone. The predicted distribution of flow is then used to predict the sediment transport over the full width of straight river channels. Deformation of the bed is calculated from solution of the sediment continuity equation. Predictions obtained in the near bank zone allow the variation in bank geometry to be simulated through time. Since bank stability is determined by the constraints of the geometry of the bank and the geotechnical properties of the bank material, channel widening can, therefore, be simulated by combining a suitable bank stability algorithm with flow and sediment transport algorithms. In combining bank stability algorithms with flow and sediment transport algorithms, there are two paramount considerations. First, the longitudinal extent of mass failures within modelled reaches must be accounted for. Second, it is necessary to maintain the continuity of both the bed and the bank material mixture in the time steps following mass failure, when the bed material consists of mixtures of bed and bank materials with widely varying physical properties. In this model, a probabilistic approach to prediction of factor of safety is used to estimate the fraction of the banks in the modelled reaches that fail in any time step. Mixed layer theory is then used to model the transport of the resulting bed and bank material mixture away from the near bank zone. Comparisons of model predictions with observations of channel geometry over a 24 year period indicate that the new model is capable of simulating temporal trends of channel morphology with a high degree of accuracy. The model has been used successfully to replicate the form of empirically-derived hydraulic geometry equations, indicating that the model is also able to predict stable channel geometries accurately. The numerical model has also been used to investigate the influence of varying the independent variables and boundary conditions on channel adjustment dynamics.