In order to analyse the propagation of fire in urban areas, we study a deterministic percolation model on a regular grid in which fire propagates from a point to a bounded neighbourhood of this point, with time constants depending on the jump. Using discrete geometry methods, we obtain an explicit formula for the propagation speed. In particular, we show that for a large time horizon, the wave front is close to the boundary of a ball with respect to a polyhedral weak-Minkowski seminorm, which can be determined analytically from the time constants. We illustrate the model by simulations on data from the Kobe fire following the 1995 Southern Hyogo Prefecture Earthquake, indicating that this deterministic model gives an accurate account of actual urban fires.