Single wall carbon nanotubes with small diameters (＜ 5.0 (A)) subjected to bending deformation are simulated by orthogonal tight-binding molecular dynamics approach. Based on the calculations of C-C bond stretching and breaking in the bending nanotubes, we elucidate the atomistic failure mechanisms of nanotube with small diameters. In the folding zone of bending nanotube, a large elongation of C-C bonds occurs, accounting for the superelastic behaviour.