The aim of this paper is to elaborate a model describing the different phases of flashover of high voltage insulators with continuous or discontinuous pollution deposits, in AC or DC. This model uses an equivalent electrical circuit. It consists of three sub-algorithms: (1) The first one is a preliminary algorithm enabling the quantification of the electrical equivalent circuit parameters based on analytical and semi-analytical formulations; (2) the second one is relative to the steady state of discharge (static sub-model), at the beginning of flashover; and (3) the third one describes the unstable mode (dynamic sub-model). The whole algorithm describes the evolution of the discharge up to flashover. It enables to determine the different parameters characterizing the discharge such as the current, length, radius, propagation velocity, linear resistance and temperature. The simulated values are found in a good agreement with the experimental ones.