A dense cloud model of avalanches is presented which includes large density difference effects as well as sediment entrainment along the path of the cloud. This model demonstrates the importance of sediment entrainment in the evolution of the front velocity. Without sediment entrainment the cloud first accelerates and then decelerates, a behaviour known from previous studies of cloud or thermal motions. With sediment entrainment the cloud is mostly in an accelerating state. The closure coefficients in the model concerning the cloud shape and air entrainment are obtained from laboratory experiments. These coefficients can be considered generic in the Boussinesq limit. A correction for inertial effects which need to be taken into account when applied to large density difference clouds such as avalanches, is proposed. An expression for the sediment entrainment coefficient is derived, taking into account the flow parameters and the sediment layer properties. The model predictions are in good agreement with recent measurement of the front velocity of a powder-snow avalanche. A presentation, in terms of dimensionless variables, of avalanche and laboratory Boussinesq cloud velocities shows clearly the similarities and differences between the two.