Abstract: This study is about a kind of ANN for applications in multivariate nonlinear regression, in order to further knowledge and understanding of discharge on an iced insulator surface and the development into a flashover AC arcs. The propagation of local arcs is necessary for a flashover to occur on an ice-covered insulator. It was supposed that the local AC arc extended when it satisfied the arc re-ignition conditions. Therefore, the minimum applied voltage for maintaining an arc burning steadily across an air gap under various conditions is a major parameter and it is referred as arc maintenance. Although ANNs have usually achieved good performances in several domains, those performances and the ANN training process are directly influenced by an appropriate choice of the network architecture. In this study an attempt has been made to model Va = f (I, L, x) for estimating the arc re-ignition conditions as estimator function of leakage current, air gap length and insulator length using multi-layer feed-forward neural network with back propagation technique and the Radial Basis Function (RBF) neural network with Orthogonal Least-Squares (OLS) learning method. A number of test results taken from the CIGELE models were simulated and analyzed and a comparison between RBF network and BP network is presented. The RBF ANNs model was found to be reliable in predicting the arc maintenance voltage, under any given set of leakage current, insulator length and air gap length. A satisfactory agreement will be observed between the simulated and experimental results.