Using the modified finite element method, the nonlinear shell-spring finite element model is established with taking the van der waals force into account. Based on the B-R motion criterion, the dynamic bucking behaviors of multi-walled carbon nanotubes are examined systemically. The dynamic critical loads for buckling and failure of double-walled carbon nanotubes under axial impact load are obtained. It is shown that in the dynamic buckling process of multi-walled carbon nanotubes, the deformation of each wall is harmonious to each other and the change of interlayer spacing is very small. The magnitude and the duration of impact load as well as the length of carbon nanotube have greater effects on the dynamic buckling of carbon nanotubes. For the shorter carbon nanotubes, asymmetrical buckling mode appears earlier. The simulations further show that the stress wave propagation in carbon nanotubes induces the asymmetrical buckling mode. In the dynamic buckling process of carbon nanotubes, there are four circumferential lobes that can be observed obviously, and their wave crest and trough of the lobes change alternately.