The two-layer concept developed previously for a liquid-solids flow has been adapted to model dense phase transport of powders in pneumatic conveying systems. Many bulk materials of this type are capable of flowing in a non-suspension moving-bed type of flow. A new model for this type of flow in a horizontal pipe has been developed where the flow is modelled as two layers: a dilute gas-solids mixture flowing above a dense gas-solids mixture. For each layer, the conservation equations for mass, momentum and energy were solved for both the gas and solids phases. In addition, mass, momentum and energy transfers between the two layers were modelled. A single pressure was shared between the two layers. The paper describes the sub-models used to describe phenomena, such as the momentum transfer between the gas and solids in a layer. Transfer of mass, momentum and energy between the two layers results in a model that behaves in a similar manner to experimental observations. For example, as the mean flow velocity increases, the depth of the dense layer decreases. The predicted pressure profile for fully developed flow was compared with experimental data. In general, the prediction of pressure profile, and the predicted depth of the dense layer show reasonable agreement with the experimental observations. A parametric study was conducted to assess the relative significance of the initial conditions on the overall behaviour of the model. Variation of the initial conditions for the same total gas and solids mass flow rates was found to have only a small effect on the prediction of fully developed flow. (C) 2001 Elsevier Science Ltd. All rights reserved.