Contamination on the surface of high-voltage outdoor insulators can lead to the formation of quasistable gas discharges, which burn in series with the resistive contaminative film. Under certain conditions, these discharges may grow to cause a complete flashover. In this paper, a model for the case of a discharge burning on a rectangular polluted strip is introduced; solution of Laplace's equation in two dimensions enables accurate values for the series resistance of the pollution film to be calculated, and a numerical method is used to calculate a factor which accounts for the change in resistance due to heating. Application of the flashover criterion di/dx > 0 to this model yields results which are in good agreement with experiment. The model can also be applied to axisymmetric insulators with complex shapes by replacing the practical insulator by its `equivalent cylinder' Good agreement is obtained between the calculated flashover voltages and those measured by the VDE 0448 test method.