Reduction, followed by hydrofluorination of uranium trioxide UO3 to produce uranium tetrafluoride UF4 is one of the stages of the French nuclear fuel making route. This dual operation is carried out in a specific reactor known as a moving bed furnace, consisting of a series of steel cylinders that form an L. In this first part of a two-part paper, the mathematical modelling of the furnace is presented in detail. The model describes solid and gas flow, heat transfer by convection, conduction and radiation in the moving bed and in the walls of the furnace, and chemical reactions. In the vertical part of the reactor, mass, momentum and energy balances are solved using the finite volume method. The horizontal part is modelled by a cascade of stirred gas and solid reactors. The assumptions and equations of the model, as well as the boundary conditions and numerical solution techniques are detailed. An example of calculated results is presented and found to agree satisfactorily with available measurements. Application of the model is discussed in Part 2. (C) 2003 Elsevier Science Ltd. All rights reserved.