  We demonstrate a novel cross-sectional deformation, called the radial
corrugation, of multi-walled carbon nanotubes (MWNTs) under hydrostatic
pressure. Theoretical analyses based on the continuum elastic approximation
have revealed that MWNTs consisting of more than ten concentric walls undergo
elastic deformations at critical pressure $p_c \simeq 1$ GPa, above which the
circular shape of the cross section becomes radially corrugated. Various
corrugation modes have been observed by tuning the innermost tube diameter and
the number of constituent walls, which is a direct consequence of the
core-shell structure of MWNTs.
