The pre-arcing regime is the rst of the two working stages which characterize the fuse operation. It commences when a fault current occurs and then it causes the melting and the vaporization of the fuselink. The pre-arcing regime ends when the fuse splits partly and when appears an electric arc. This work deals with the modeling and the numerical simulation of the physical phenomena observed during pre-arcing regime. We propose in this study an electro-thermal model coupling electrical and ther- mal aspects of physics observed. The heat transfer equation used an enthalpy for- mulation to describe phase transitions in the fuse element where a Laplace equation for the scalar potential and the Ohm law permit to obtain the current density and the Joule e ect. For space discretization we use a nite element method where a Cherno scheme is used for time discretization. The advantage of this model is to take into account the dependence of the transport coe cients with temperature. First results led in the case of a single 2D fuse wire show that pre-arcing time de- pends closely to the circuit parameters and to the geometrical form of the reduced sections of the fuse element. Industrialists used a well-known empirical coe cient which permit the calculation of the pre-arcing time when the fuse is submitted to high fault currents. To take into account the heat losses to the surrounding of the fuse, we use in the one hand a 3D model of the fuse element where heat losses are taken as boundary conditions and in the other hand we modeled the porous media by a homogeneization technic. Main di erences were observed between the pre-arcing times give by simulations and those give by experiments. Further works should be necessary in order to study the in uence an electromechanical force which probably causes the splitting of the fuse element.