In this paper, the principal pollution flashover models are reviewed and then an impedance criterion for are propagation is proposed. This criterion differentiates the case in which the are elongates until total flashover occurs from the case in which the are stops before it reaches the end of the insulator. It is shown that the Hampton criterion is not a sufficient condition for initiation of the are. Indeed, the latter can expand, under certain conditions, even if the Hampton criterion is not satisfied. An analytical model allowing one to determine the critical voltage that insulators can withstand is also established. This is based on an energetic balance, an equivalent electrical circuit and the physical characteristics of the are. The critical voltage, the critical current and the critical are length for polluted insulators are calculated using the elaborated model. The results so obtained are found to be in accordance with the experimental ones represented by known empirical relations.