By formulating the fundamental electromagnetic (EM) equations in terms of the stream potential of the surface current density, we can express the EM response of a rectangular thin plate as the solution of a single equation subject to simple boundary conditions. A finite difference approximation of this equation reduces the problem to that of solving a large set of linear algebraic equations. The solution of these equations by a modified Gauss-Seidel iterative method yields the stream potential and thus permits visualization of the eddy currents circulating inside the plate conductors. The secondary field calculated from the stream potential compares well with that given by scale model measurements provided that the grid spacings used in the finite differences are small enough. Using a further approximation, we can also simulate inductively thick conductors if the conductors are not geometrically thick.