This paper reports high-resolution electron microscope (HREM) observations and atomistic simulations of the bending of single and multi-walled carbon nanotubes under mechanical stress. The study shows that single and multi-walled nanotubes can be bent to large angles without breaking, due to the remarkable flexibility of the hexagonal carbon lattice. The bending process is fully reversible up to angles exceeding 110 degrees, with the only effects being stretching of the outer side and compression of the inner side. Beyond this angle, a buckling pattern emerges, leading to periodic disruptions in the lattice structure. The simulations reveal that the formation of kinks is a key feature of the bending process, with the number of kinks increasing with further bending. The study also shows that the deformation of nanotubes is likely introduced during handling, such as transferring them to the TEM specimen grid. The simulations, using a realistic many-body potential for carbon atoms, reproduce the HREM images and provide detailed atomistic information about the bending process. The results indicate that the hexagonal network is preserved up to about 110 degrees, with bond-breaking occurring only at angles exceeding 120 degrees. The critical curvature for kink formation is found to be independent of the tube's length and is well described by a mathematical equation. The study also shows that double-walled nanotubes exhibit more complex buckling patterns, with the formation of multiple kinks. The simulations confirm that the nanotubes retain their graphitic structure even at large bending angles, showing substantial promise for structural and fiber applications.This paper reports high-resolution electron microscope (HREM) observations and atomistic simulations of the bending of single and multi-walled carbon nanotubes under mechanical stress. The study shows that single and multi-walled nanotubes can be bent to large angles without breaking, due to the remarkable flexibility of the hexagonal carbon lattice. The bending process is fully reversible up to angles exceeding 110 degrees, with the only effects being stretching of the outer side and compression of the inner side. Beyond this angle, a buckling pattern emerges, leading to periodic disruptions in the lattice structure. The simulations reveal that the formation of kinks is a key feature of the bending process, with the number of kinks increasing with further bending. The study also shows that the deformation of nanotubes is likely introduced during handling, such as transferring them to the TEM specimen grid. The simulations, using a realistic many-body potential for carbon atoms, reproduce the HREM images and provide detailed atomistic information about the bending process. The results indicate that the hexagonal network is preserved up to about 110 degrees, with bond-breaking occurring only at angles exceeding 120 degrees. The critical curvature for kink formation is found to be independent of the tube's length and is well described by a mathematical equation. The study also shows that double-walled nanotubes exhibit more complex buckling patterns, with the formation of multiple kinks. The simulations confirm that the nanotubes retain their graphitic structure even at large bending angles, showing substantial promise for structural and fiber applications.