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In the study described herein, we observed the buckling behavior of carbon nanotube (CNT) bundles under axial compression using molecular dynamics (MD) simulations. We found that the critical buckling loads of CNT bundles are much higher than that of an individual single-walled carbon nanotube (SWCNT). The addition of SWCNTs into a CNT bundle results in as much as a fivefold increase in its buckling load. The long-range van der Waals interactions also improve the overall rigidity of the CNT bundles. The larger the CNT bundle, the greater the significance of the van der Waals interactions. We also found that the buckling load of a CNT bundle is directly proportional to that of a SWCNT.