The penetration of leakage flux into a laminated machine or transformer core is governed by the currents induced in the steel, and poses an anisotropic and 3-dimensional field problem which is also severely nonlinear. It is shown that the differential equations can be formulated in terms of an electric vector potentialT, and magnetic scalar potential Ω, and that the solution can be expressed in the form of three different characteristic modes, two associated with the core surfaces and the third describing the flux penetration into the interior. This form of solution provides both a qualitative and quantitative picture of the 3-dimensional flux paths, and eddy current loss distribution, and also a practicable means of allowing for saturation. The result can be expressed in the form of a simple network model that is well suited to numerical solution by computer.