A computational fluid dynamic (CFD) study is combined with an experimental program to develop a model of burning rate and extinction in fires. The ultimate objective is to predict extinguishment by water droplets and thereby determine the water requirement for the extinction of actual fires. The experimental program is conducted in a full-size are gallery with a commercial sprinkler system installed in the roof. Water droplet size distribution, velocities and mass flux from the sprinkler are measured as inputs for the computations. Horizontal sheets of polymethylmethacrylate 1 metre square are uniformly ignited and burned in a draft of about 1 m/s. Burning rates are monitored by load cell and when the fire is well established, the sprinkler is actuated. A video record of the extinguishment together with thermocouple and heat flux measurements are used to time the event and to describe the process. The primary extinguishment mechanism is considered to be due to the cooling of the burning PMMA surface below its vaporisation temperature. The effective heat transfer rate from water droplets to the hot surface is therefore important, and it is measured in a separate series of experiments on a heated steel plate. It is found that droplet dynamics on the limited size surface reduce the effective heat transfer by up to two-thirds of the maximum. The CFD model, coupled to the solid surface, predicts the unsteady increase in burning rates and then the extinguishment of the surface. A lagrangian particle model and discrete transfer radiation model supplement the gas phase equations of motion, energy and species concentrations. The predictions of burning rate are reasonably good and are sensitive to modelled radiative Feedback, a function of modelled soot concentrations. Extinguishment occurs regressively, but rapidly From the plate leading edge. The model is able to give a good representation of the extinction process and duration.