River dynamic behaviour is affected by variations both in the water phase and in the transported sediment phase. A change in the water regime may lead to significant morphological changes in the bed profile, which in turn may strongly influence the flow conditions. Transcritical flows over mobile beds are particularly challenging to model due to the rapid variation in space and time of the solid transport, and to the specific treatment required for boundary conditions. The one-dimensional numerical model presented in this dissertation divides the flow in two fully coupled layers: a water layer and a water-sediment transport layer. This model was initially designed to depict dam-break flows, which does not require a specific treatment of boundary conditions. An extension of the two-layer approach is proposed in order to properly take into account boundary conditions. The treatment of boundary conditions commonly relies on characteristics. Within a two-layer model, which embodies five governing equations, an appropriate eigenstructure analysis is developed based on numerical estimations. This novel approach results in a new characterization of the critical stage by defining a specific two-layer Froude number. The model is compared to the classical Saint-Venant – Exner approach and favourably applied to several typical situations: uniform flow, which allows a straightforward calibration of the model parameters; regressive erosion around a mild-to-steep slope transition; evolution of a mobile bed under a hydraulic jump; and scour hole formation downstream of a fixed bed.