  Quantum oscillations have long been regarded as the manifestation of the
Fermi surface in metals. However, they were recently observed in Kondo
insulators. We examine the Kondo screening due to Landau levels in Kondo
insulators. It is shown that even for large Kondo insulating gaps, appreciable
amplitudes of quantum oscillations that are consistent with experimental
observations are present both in magnetization and resistivity. Specifically,
we show that due to the periodic alignment between the Landau levels in the
conduction and the f-orbit electrons, the Kondo screening itself undergoes
oscillations so that the electronic structure oscillates with the magnetic
field. Our results explain main features of quantum oscillations observed in
experiments. They indicate that the non-rigidity of the electronic structure
results in observable quantum oscillations Kondo insulators. This new effect
provides a new way to probe the Fermi surface geometry of insulators.
