IT has been suggested(1) that the tensile strength of carbon nanotubes(2) might exceed that of other known fibres because of the inherent strength of the carbon-carbon bond. Calculations of the elastic properties of nanotubes confirm that they are extremely rigid in the axial direction and are most likely to distort perpendicular to the axis(3,4). Carbon nanotubes with localized kinks and bends(5,6), as well as minor radial deformations(7,8), have been observed. Here we report the existence of multi-shelled carbon nanotubes whose overall geometry differs radically from that of a straight, hollow cylinder. Our observations reveal nanotubes that have suffered complete collapse along their length. Theoretical modelling demonstrates that, for a given range of tube parameters, a completely collapsed nanotube is favoured energetically over the more familiar ’inflated’ form with a circular cross-section.