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This paper focuses on the growth and spread stage of full-scale fires in enclosures, where a localized flame spreads across a single fuel item, increasing the heat release rate, thereby resulting in increased fire hazard. The development of a numerical model for fire spread over a solid fuel surface, and its integration into a CFD model, is described. The conflicting demands of resolving the small scale flame front phenomena while simultaneously accounting for the large-scale enclosure flow phenomena are addressed. The surface of the fuel is descretised with a regular square array, and flame spread occurs as a series of ignitions of surface elements. Ignition of an element is determined by a combination of critical surface ignition temperature and cellular automata techniques. Regression of the combusting fuel surface is modeled, with a fine grid retained at the fuel surface by allowing the grid to "collapse" with the surface. A grid transformation is applied to restore orthogonality of the collapsed grid, for simple computation of the heat equation. The flame spread model has been designed to be independent of geometry, although experimental validation exercises are carried out for radial spread over horizontal surfaces only. Predictions are made for the burning of a slab of polyurethane foam in a full-scale multi-room experimental building-fire facility. The predictions compare favorably with the experiments, indicating the broad validity of the methods used in flame spread model.