The growing scarcity of dumping sites for municipal solid waste, and the increasing environmental problems associated with landfill waste, have led to more stringent regulations and high costs of waste disposal. In the UK, landfill tax is designed to encourage energy-efficient waste-managements strategies aimed at reducing the amount of landfill waste through incineration, while maximising the recovery of waste energy. However, at present, reliable data and fundamentally based design procedures are not available to assist the design and manufacture of incinerators. The development of computational fluid dynamics (CFD) provides a means of modelling the gas-phase region in conventional incinerators, but the open literature contains no model that can accurately predict the conditions within a solid bed. Consequently, operation or control of municipal waste incinerators is still based on empirical relationships. Further research into secondary combustion, concerning the destiny of contaminants and emissions, for example, is inhibited by lack of knowledge of fundamental data and techniques for modelling the processes that occur inside the burning bed of refuse. This paper describes the foundation of a mathematical model for the burning of municipal solid waste on a travelling-grate incinerator.