The entry and subsequent breakup of the ~17–20 m diameter Chelyabinsk meteoroid deposited approximately 500 kT of TNT equivalent energy to the atmosphere, causing extensive damage that underscored the hazard from small asteroid impacts. The breakup of the meteoroid was characterized by intense fragmentation that dispersed most of the original mass. In models of the entry process, the apparent mechanical strength of the meteoroid during fragmentation, ~1–5 MPa, is two orders of magnitude lower than the mechanical strength of the surviving meteorites, ~330 MPa. We implement a two‐material computer code that allows us to fully simulate the exchange of energy and momentum between the entering meteoroid and the interacting atmospheric air. Our simulations reveal a previously unrecognized process in which the penetration of high‐pressure air into the body of the meteoroid greatly enhances the deformation and facilitates the breakup of meteoroids similar to the size of Chelyabinsk. We discuss the mechanism of air penetration that accounts for the bulk fragmentation of an entering meteoroid under conditions similar to those at Chelyabinsk, to explain the surprisingly low values of the apparent strength of the meteoroid during breakup.