Abstract. A distinguishable feature of overland tsunami propagation is the incorporation of solids within the flow column, either sediment from the natural environment or remains from built infrastructure. This article describes a 2DH (two-dimensional horizontal) mathematical model particularly suited for tsunami propagation over complex and dynamic geometries, such as river and estuarine mobile beds. The discretization scheme is based on a finite-volume method using a flux-splitting technique featuring a reviewed Roe–Riemann solver, with appropriate source-term formulations to ensure full conservativeness. The model is validated with laboratory data and paleo-tsunami evidence. As a forecasting application, it is applied to a tsunami scenario in the Tagus estuary, an effort justified by the numerous catastrophic tsunamis that are known to have struck this location over the past two millennia. The obtained results show that, despite the significant differences in Lisbon's layout and morphology, a 1755-like tsunami would still inflict a devastating impact on this major city.