Electrically conductive ferromagnetic shielding materials exhibit nonlinear behavior (including magnetic saturation) under intense pulsed electromagnetic field conditions. This paper considers the fundamental problem of a long, thin-walled cylindrical electrically conductive ferromagnetic shield subjected to axially-directed, unipolar, short-duration surface current pulses. A simple idealized relative differential magnetic permeability model is used to portray the nonlinear effects of a field-dependent permeability, including saturation. The transient magnetic field intensity within the shield is investigated using finite difference time domain (FDTD) calculations.