This paper discusses diffusion of a pulsed magnetic field into a resistive element fabricated from a low-carbon steel. The developed numerical model shows that the process of the magnetic field diffusion into the steel at the leading edge of the pulse can be conventionally described by three stages: initial stage extending up to saturation of the steel surface layers, stage of saturation when the discharge current diffuses into the bulk of the steel, and stage of conduction when the discharge current is distributed practically uniformly in the steel. Approximate analytical relations describing the voltage drop across the resistive element are derived for each of the three stages. These relations are used for estimation of the effect of the ferromagnetic properties of the steel on transients in electrical circuits with the resistive element. Experiments prove the validity of the obtained analytical results.