  Stable cross-sections of multi-walled carbon nanotubes subjected to
electron-beam irradiation are investigated in the realm of the continuum
mechanics approximation. The self-healing nature of sp$^2$ graphitic sheets
implies that selective irradiation of the outermost walls causes their radial
shrinkage with the remaining inner walls undamaged. The shrinking walls exert
high pressure on the interior part of nanotubes, yielding a wide variety of
radial corrugation patterns ({\it i.e.,} circumferentially wrinkling
structures) in the cross section. All corrugation patterns can be classified
into two deformation phases for which the corrugation amplitudes of the
innermost wall differ significantly.
