This paper describes the dynamic model of the hot section of an incineration plant with steam production. The model is based on a first-principles approach that starting from material, energy, and momentum balances leads to the integration of a differential-algebraic system of 132 equations. The hot section of the plant comprises a furnace, a postcombustion chamber, and a waste heat boiler. The reciprocating grate kiln represents one of the most important features of the process, where the heterogeneous combustion of waste takes place. The waste, coming from diverse collections, is transferred from the pit into a vertical hopper and enters into the furnace pushed by a discontinuous feeding grate. Also the burning waste is discontinuously moved through the primary combustion chamber by reciprocating grates. These discontinuous features are mainly responsible for the high oscillations of process variables. The model was implemented for control purposes with the aim of reducing oscillations and offsets through a model-based control system. The paper describes thoroughly the key points that were addressed in structuring and solving the numerical detailed model. Finally, a validation procedure sketches a quantitative comparison between experimental measured data and simulated values. The measured process variables were acquired on-line from the real-time database running on the distributed control system.