Fuel elements consisting of beds of coated particles cooled directly by helium are of special interest for gas-cooled fast reactors. The thermal design of such elements depends decisively on the distribution of flow through the bed. A theoretical model is presented for calculating this distribution, including the cases of ducts with variable cross sections and beds of variable porosity. Pressure, velocity and flow distributions were measured in rectangular ducts with constant and variable cross-sectional areas at different Reynolds numbers and transpiration rates. The results are in reasonable agreement with computer predictions based on the theoretical model.