Abstract : During last years, several numerical formulations have been developed by us to model physical problems such as: conducting film effects on the surface of insulators (pollution), high frequency eddy-currents, earth field effects on the hull of a ship. The physical effects are completely different, but in each of these examples, they originate from a region thin relative to the other geometrical dimensions. An efficient numerical approach consists of using a surface representation with special boundary conditions expressing the solution inside the thin region. We propose in this paper a didactical approach to thin regions in electromagnetics and, as an example, the boundary conditions and surface equation for eddy currents flowing inside a thin ferromagnetic shell. The numerical tests are done using the BEM software PHI3D, but the results could easily be transposed in a FEM context. The practical applications may concern the computation of losses (shield of electrical machines or transformers) or low frequency electromagnetic perturbations (screen effects, EMC) as well as special applications like optimisation of the induction heating of pans (French "art culinaire").