A numerical computer model, Transient Inundation Model for Rivers -- 2 Dimensional (TrimR2D), that solves the two-dimensional depth-averaged flow equations is documented and discussed. The model uses a semi-implicit, semi-Lagrangian finite-difference method. It is a variant of the Trim model and has been used successfully in estuarine environments such as San Francisco Bay. The abilities of the model are documented for three scenarios: uniform depth flows, laboratory dam-break flows, and large-scale riverine flows. The model can start computations from a ?dry? bed and converge to accurate solutions. Inflows are expressed as source terms, which limits the use of the model to sufficiently long reaches where the flow reaches equilibrium with the channel. The data sets used by the investigation demonstrate that the model accurately propagates flood waves through long river reaches and simulates dam breaks with abrupt water-surface changes.