We present a mathematical model for simulating the steady-state behaviour of a moving bed furnace used in the French nuclear fuel making route. This furnace is a counterflow gas-solid reactor which converts uranium trioxide UO2 into uranium dioxide UO2 then into uranium tetrafluoride UF4. The model describes most of the physico-chemical phenomena occurring into the reactor by coupling a mechanistic approach (for the vertical part of the furnace) and a systemic one (for the horizontal part). The equations are solved by a numerical code specifically developed. The first results obtained with an industrial reference set of operating parameters are discussed. Then, the influence of some of those operating parameters is studied with the help of the model.