This paper presents a generalized solution to modelling hydraulic erosion using ideas from fluid mechanics. The model is based on the Navier–Stokes equations, which provide the dynamics of velocity and pressure. These equations form the basis for the model to balance erosion and deposition that determine changes in the layers between water and erosion material. The eroded material is captured and relocated by water according to a material transport equation. The resulting model is fully 3D and is able to simulate a variety of phenomena including river meanders, low hill sediment wash, natural water springs and receding waterfalls. The simulations show the terrain morphogenesis and can be used for animations as well as for static scene generation. Copyright © 2006 John Wiley & Sons, Ltd.