The limiting nonlinear analysis of Sixtus and Tonks[1] is extended to the prediction of the shielding effectiveness of soft magnetic materials subjected to electromagnetic pulses. The magnetization curve is approximated by N steps in which magnetic induction or intensity varies but both never vary simultaneously. This method is applied to cylindrical magnetic shields. When applied magnetic intensity exceeds a certain value a corresponding value of magnetic induction is imagined to form at the surface and propagates inward. As the applied field is increased successive regions of corresponding magnetization propagate. By the use of Maxwell's curl equations, N simultaneous nonlinear first order differential equations are established and solved to yield the transient distribution of magnetic induction and electric field intensity. An experimental verification of this method is made by discharging a 3 μ f capacitor charged to 30 kilovolts into a 50 Ω triaxial transmission line comprising a 61 cm long middle conductor made of 80% NI-iron and copper inner and outer conductors. The line is matched in its characteristic impedance to minimize ringing. The electric field passing through the thickness of the ferromagnetic tube is monitored by an oxcilloscope separated from the energy source by an iron clad shielded room. The experimentally measured electric fields penetrating the ferromagnetic tube agree with those predicted by the approximate physical model within the bounds of experimental accuracy.