Thin layers of magnetic substance are often used in magneticshieldings. Since the scale of the spatial change in electromagneticfields in the direction of the thickness of such a thin layer isconsiderably different from that in the transverse directions, thenumerical treatment of the interior electromagnetic fieldsis formidable. In this paper, it is shown that the impedance boundary conditionson the surfaces of the thin magnetic layer, which have been written informer papers by the scalar potentials, can be expressed in terms ofthe vector potentials.Moreover, a new numerical method for analysis of eddy currents on thin magnetic layersis introduced, inwhich the quasi-static magnetic field in an air regionambient the thin layer is analyzed by solving the boundary integralequations under the impedance boundary conditions without any numericaltreatment of the interior field. This formulation has no difficultieseven when the skin depth is very short compared with the thickness ofthe layer. It is shown that the numerical results obtained by the presentmethod in two-dimensional and axisymmetric systems agree well withthe results analytically obtained or computed by a conventional numericalmethod.