The nonlinear mathematical model for depth-averaged flow allows for discontinuous solutions that correspond with the dynamic behaviour of rapid changes in flow. Such discontinuities, that can fundamentally affect the predicted morphological response of a river, are analyzed theoretically and numerically. Hereto, the entropy conditions as defined by Lax and the Rankine-Hugoniot or shock relations are used to analyze propagation rates and stability. Apart from subcritical and supercritical flows, a transition regime can be identified for flows with mobile beds.