The authors present a new method to compute the current distribution (eddy currents or conduction currents) in a solid or liquid material with boundaries made of another thin and conducting material. In this configuration numerical method such as finite element techniques are unavailable due to the thickness of the boundary to be meshed. The authors propose to use à special finite element called "boundary element" and to introduce the characteristics of the containing medium into the boundary conditions applied to the main conducting material. The techniques for solving problems with such mixed boundary conditions are exposed and results for some conduction problems are given.