This work deals with the calculation of pre-arcing time in the case of High Breaking Capacity fuses submitted to high fault currents. The fuse elements studied consist of silver fuse strips with reduced sections in their centre. During the fuse working the fuse element is fused partly and hence vaporized. The time necessary to obtain an electric arc is called the pre-arcing time. This latter is defined by the duration from the appearance of the fault current to the splitting of the fuse element due to the vaporization of the reduced sections. The mathematic model is based on the solution of the heat transfer equation, using an enthalpy formulation to take into account the phase transitions, supplemented by an energy source due to the heat produced by ohmic losses. In order to determine the current density evolution in the fuse element, the Laplace equation governing the electric potential and the Ohm's law are used. Two typical fuse elements close to industrial ones are chosen for the simulations. The calculated pre-arcing times are given together with the main electrical properties, and compared with the experimental values. The resistive case with cos phi ~ 0.9 is discussed for a 2.5 mm and 7.5 mm-width elements respectively with one and three reduced sections.