The paper presents a simple mathematical model for sediment transport in straight alluvial channels. The model, which is based on physical ideas related to those introduced by Bagnold (1954), was originally developed in two steps, the first describing the bed load transport (Engelund 1975) and the second accounting for the suspended load (Fredsøe and Engelund 1976). The model is assumed to have two advantages as compared with empirical models, first it is based on a description of physical processes, secondly it gives some information about the quantity and size of the sand particles in suspension and the bed particles.