In this paper we present a numerical model in which both the thermal and the electromagnetic aspects of the over-critical current regime of HTS materials are taken into account. The electromagnetic and thermal equations have been implemented in finite element method (FEM) software in order to obtain a novel, closer to reality model for investigating the behaviour of the materials when the current exceeds Ic. A thermal dependence of the electrical parameters, like the critical current density Jc, has been introduced. This model has been used to analyse the behaviour of strip lines of a YBCO/Au fault current limiter (FCL) on a sapphire substrate. Simulations with currents largely exceeding Ic have been performed, showing that the current limitation phase can be correctly reproduced. Such modelling can be used to study the influence of the geometry on the performance of the FCL. It is designed to replace experiments with currents far exceeding Ic which may damage or destroy HTS samples or devices.