A system of differential equations that describe the growth of a forest fire front in time for variable fuel, weather and topographical conditions is derived. The system is first order, non‐linear and contains parameters that can be obtained from forestry data. A finite difference solution is presented, together with its inherent problems and their solution. Results are presented for a variety of situations that include variable fuel, wind and fire breaks. It is found that the equations and their solution efficiently produce simulations for complex problems.