Stability test of nanotubes with presence of single vacancies has been performed by means of tight-binding molecular dynamics and electron-ion dynamics within the framework of the density functional theory. A 4A diameter nanotube having a single vacancy with three dangling bonds has been found to retain its cylindrical shape under high temperature around 4000K, despite its large internal strain energy. Meanwhile, an electronic excitation of vacancy-related state has shown considerable atomic displacement, which may cause extraordinary large lattice vibration or nanotube decay. Furthermore, the single vacancy can stabilize itself by making carbon dimer to remain with only one dangling bond. Narrower nanotubes tend to prefer this self-stabilization and thus could be tolerant to the presence of defects.