This paper presents a continuous finite element model for shallow water equations coupled with a bedload sediment conservation law. The model incorporates a sign-preserving conservative correction based on the flux correction transport methodology. Complete algorithm permits simulation of flows with evolutionary boundaries and erodible–non erodible interfaces under severe conditions without spurious mass exchanges and oscillations. Numerical experiments explore the efficacy of the procedure for dam-break problems on channels with dry beds, for partially and totally erodible beds, and for migration of small bedforms. Computation of real river morphodynamics under intense flooding illustrates practical application of the model.