Unlike the protection systems with electromechanical action protection, the fuses have the advantage of sure protection. Designing fuses requires a high accuracy for determining the current field density and the temperatures from the fuse-elements, till they melt. In order to have zero divergent of the current density the paper employs a FEM procedure in which the electrical vector potential is implied. Special shape functions are used for holes in the case of multiply connected structure. The electric problem is coupled with thermal field one.