We carry out systematic molecular mechanics (MM) analyses to study the effect of the displacement increment on the critical buckling strain of single-walled carbon nanotubes (SWCNTs) under axial compression. The SWCNT geometric parameters, such as the tube length, diameter, and chirality, are varied in the numerical studies. The results show that the critical buckling strain of the SWCNTs deduced from the atomistic analyses is highly sensitive to the displacement increment used in the numerical simulation, and such an effect is more obvious for tubes with smaller diameters. Therefore, a reasonable compressive displacement increment should be selected in the atomistic simulations in order to obtain the intrinsic values of the critical buckling strain, which is suggested in this paper. The studies in this paper may be used to explain the contradicting results of the critical compressive buckling strains computed by other MM analyses in the literature. © IOP Publishing Ltd.