Carbon nanotubes subject to large deformations reversibly switch into
different morphological patterns. Each shape change corresponds to an
abrupt release of energy and a singularity in the stress-train curve.
These transformations, simulated using a realistic many-body potential
, are explained by a continuum shell model. With properly chosen param
eters, the model provides a remarkably accurate ''roadmap'' of nanotub
e behavior beyond Hooke's law.