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Computational river models are in widespread use for estimating flood extent and the effectiveness of proposed flood mitigation schemes. This paper investigates the application of commonly used computational models to river floods, highlighting the advantages and shortcomings and current research activity. 1D, quasi‐2D, 2D, and 3D computational models are applied to simulate a large‐scale physical model tested in the Flood Channel Facility (FCF), Wallingford, as well as field data from the River Severn near Shrewsbury. The results reveal that commonly used 1D models give a reasonable representation of flood levels and flood extent but do not include floodplain/main channel interaction losses associated with compound flows and can be in error in their predictions. This deficit can be overcome in a straightforward manner by using a modified conveyance at each cross section based on the depth‐integrated turbulent form of the Navier–Stokes equation. This so‐called Lateral Distribution Method (LDM) has been incorporated into a new Conveyance Estimation System (CES) funded by the EA/Defra Joint Research Programme in Flood and Coastal Defence and developed by HR Wallingford Ltd for use with 1D models. Alternatively, 2D models can be more useful when simulation of flood inundation extent is important. The use of 3D models is becoming more common due to their ability to simulate very complex flow patterns over short river reaches. Initial results indicate that the choice of mesh discretization in a 3D model has a significant influence on the ability of the model to reproduce secondary velocity fields correctly. Problems of data requirements, friction and free surface representation still persist in 3D models in general.