AbstractWaste management has become a major concern world‐wide and incineration is now being increasingly used to treat waste which cannot be economically recycled. The combustion of conventional well specified fossil fuels is a very complex process since it involves two‐phase turbulent reacting flow including radiant heat transfer. Incineration is even more complex since the waste is poorly specified and its composition varies from moment to moment. In the past, the design of incinerators has not been based on fundamental understanding and modelling of the process, and empirical rules have had to be used.Over the last few years, computational fluid dynamics (CFD) has provided a means to model the freeboard region in a conventional municipal solid waste incinerator but the open literature contains no rigorous fundamentally based model of the bed region. The prediction of the flow composition emerging from this region is particularly important since it provides the “upstream” boundary condition for the flow calculations in the freeboard. For example, the calculation of the subsequent history of heavy metals requires knowledge of their emission rate from the burning bed.The processes in the bed include drying, pyrolysis, oxidative burning, and gasification of the char. Furthermore, the movement of the grate is designed to mix the waste as it burns. Indeed, the existence of a rigorous bed model would also permit the grate design to be optimised, and, if immediate data on the feed were available, a rational combustion control strategy could be devised. A preliminary model of combustion in the bed is proposed herein based on governing equations for the burning of individual “regions” of waste in the upward gas flow, their motion, and radiant heat transfer within the bed. The emissions of gases from the surface of the bed is very non‐uniform with oxygen emitted from either end of the bed, organic compounds from the one‐third region, and carbon monoxide from the centre. The surface layer of this central part of the bed consists of char with gases coming up from the oxidising layer below containing NOx derived from the fuel nitrogen. The char region therefore acts as an important reburn zone and it is suggested that this reduces some of the NOx to nitrogen. This is important since the minimisation of NOx by optimising the basic combustion process is likely to be environmentally preferable to subsequent control of NOx by the injection ofreactants such as ammonia.The calculation of flow and combustion in the freeboard using CFD can quantify the consequences of design concepts, however guidelines are needed to devise specific design concepts which are worthy of investigation. Thus the computer cannot “invent” a design but it can quantify the results of ideas.Incinerator design thus requires a judicious combination of fundamental combustion science, ingenious engineering guided by an understanding of the mixing process, and last but not least, practical experience of previous failures and successes.