This work presents a comprehensive mathematical model of a fixed bed gasifier, where heat and mass transport resistances and chemical kinetics are accounted for both at the reactor and the particle scale. A multistep kinetic model of devolatilization of solid fuels, such as coals, plastics, biomasses and wastes has been employed and validated. The kinetic model of refuse derived fuels (RDF) and wastes is simply based on a linear combination of the devolatilization models of its main constituents. Ligno-cellulosic and plastic materials, together with ash and moisture, allow to account for the high heterogeneity of RDF. Successive gas phase reactions of the released species are described with a detailed kinetic scheme. Furthermore, an accurate description of heat and mass transport between gas and solid phases allows the proper characterization of combustion and gasification of the solid fuel at the particle and reactor scale. The mathematical model of a counterflow fixed bed reactor is then applied first to discuss the importance of heat transfer resistances at the particle scale, then to describe coal and biomass gasification. This work summarizes several facets of this problem with validations and examples and it allows to evaluate feasibility and limitations of the proposed approach.