A box model for instantaneous release and subsequent one-dimensional spreading of isothermal dense gases on sloping surfaces is presented. A numerical solution and an approximate analytical solution of the model equations are compared to the experimental data obtained in a sloping heavy-gas channel of the Institute of Fluid Dynamics at ETH-Zurich. The influence of the rear wall of the containment from where the cloud is released is analysed. Different entrainment assumptions, in particular the scaling of the entrainment parameters, are discussed. The numerical values of the entrainment parameters are tuned by computer optimization in order to obtain best agreement of the theoretical results with experimental data.