The dynamic buckling caused by propagation of a stress wave in single-wall carbon nanotube subjected to impact torque is investigated. The single-wall carbon nanotube is modeled by a cylindrical shell with semi-infinite length, and the dynamic buckling under impact torque is reduced to a bifurcation problem caused by the propagation of torsion stress wave. The bifurcation problem can be converted to solving a group of nonlinear algebraic equations. The numerical computation is carried out, and the effects of the different parameters on dynamic buckling are discussed. It is found that if critical buckling time of the carbon nanotube is different, the corresponding buckling model is different, too. Relation between the critical buckling stress and the critical buckling time is given. Molecular-dynamic simulations of torsional deformation of a single-wall carbon nanotube have been used to obtain the critical buckling strain, which is 0.064. In this work, the critical buckling strain obtained by the continuum model is 0.061, which is very close to the value 0.064. Single-wall carbon nanotubes have very much powerful anti-impact torque, and the critical buckling shearing stress can reach up to 132GPa.