- Spatially nonuniform fluctuations of external magnetic field are typically present in applications of superconductors as magnetic bearings and shields. We use the Bean critical- state model to analyze penetration of such alternating fields into type-II superconductors. Simple asymptotic solutions are found for infinite slab configuration and low penetration depth of the magnetic field. To calculate AC losses, we use a vector potential formulation. The solutions obtained are tested by numerical simulations, based on a variational reformulation of the critical-state problem, and by experiments. A BSCCO superconducting bulk specimen with power law voltage–current characteristic was used in experiments.