A mathematical model for a lit cigarette is derived, which predicts pressure, flow velocity, temperature and gas concentrations inside and outside the cigarette. It consists of a continuum-mechanical model for the flow and a discrete model for the chemical reactions occurring in the tobacco particles. The cigarette model is simulated for a cigarette in a vertical position by methods known as computational fluid dynamics (CFD). Calculated temperature and gas concentration profiles are compared to measured data from the literature for smouldering, puffing and steady-draw. For thermophysical properties, such as temperature fields and burn rates, a good correspondence with experimental data was found. The correspondence with measured gas concentration profiles was also acceptable, even though the reaction model is rather simple. The results show the importance of including the surroundings of the cigarette in the computational domain. Secondly, a cigarette in a horizontal position is simulated both for free smouldering and for smouldering on a substrate, as occurs, for example, during the ignition strength test. The results show certain qualitative differences between the two smouldering regimes in the flow pattern outside the cigarette and in the transfer of heat to the surroundings and to the substrate. The proposed model offers two main advantages. Firstly, it does not need the input of any data, that can only be measured if the cigarette has been lit, such as temperature fields or burn rates. Secondly, with this model all types of smoking regimes such as smouldering, puffing and steady-draw can be simulated without making any modifications to the mathematical model or its parameters. Only the boundary conditions need to be adapted.