After a brief classification of the numerical methods used for the solutions of the electrical problems governed by differential equations of the Laplace-Poisson type, the mathematical formulation of the Boundary Element Method is set out. Some operational details are given for this method, that concern the use of zero order, of the first and of the second order. The leakage field of a transformer having been considered, a comparison is finally made between the results obtained by this method and those obtained using the Finite Element Method, in order to get some indications as to the possibilities of the use of the method itself.