This paper studies the dynamic buckling behavior of multi-walled carbon nanotubes (MWNTs) subjected to step axial loading.A buckling condition is derived,and numerical results are presented for MWNTs under fixed boundary conditions.It is shown that the critical buckling load of M WNTs is of multi-branches and decreases as the time elongates.The associated buckling modes for different layers of MWNTs can be either in-phase or out of phase,which is related to the branch that the critical buckling load belongs to.For MWNTs with the same innermost tube radius,the critical buckling load is decreased when increasing the layers.