A computer-based model of a small smouldering or creeping forest fire has been designed to simulate burned and burning areas of a fire at any time after ignition. The model assumes that a fire spreads in a grid whose squares are homogeneous fuel types. The arrangement of fuel types within each grid for a specific cover is determined by a probability distribution and a Monte Carlo sampling procedure. Rates-of-spread of fire in each fuel type vary with changes in fuel moisture. Persistence time of fire in each fuel type is considered. The minimum time required for the fire to reach any square in the fuel grid is determined by a dynamic programming algorithm. Rates of spread are allowed to vary during the life of the fire.