Abstract: The buckling behavior of single-wall carbon nanotubes（SWCNTs）under compression is simulated by using the molecular dynamics method with Tersoff-Brenner potential to describe the interactions between atoms in SWCNT. The results show that the Young's modulus of SWCNTs decreases as the radius of SWCNTs increases，and critical stress and critical strain when the buckling of SWCNTs occurs are related to the slender ratio of SWCNTs. The difference of slender ratio determines two different buckling modes. The global buckling first happens for SWCNTs with the smaller slender ratio，while the local buckling first occurs for those with the larger slender ratio. The critical stress in the global buckling is proportional to the inverse of length of SWCNTs，while the critical stress in the local buckling is inversely proportional to the radius and the square of length of SWCNTs，which shows that the buckling theory of circular cylindrical shell in continuum mechanics can not be directly applied to the buckling of SWCNTs.