Abstract: By use of the method of the preferred mode, theoretical analyses of dynamic buckling for elastic bars subjected to axial compression, with the loaded end clamped but movable in axial direction or simply supported, were performed. The supposed buckling modes fulfill not only the boundary condition, but also the supplementary restraint equation given in literatures. Research shows that the critical-load parameter and the dynamic characteristic parameter of the most amplified mode are in accordance with the results given by the Twin-characteristic-parameter solution. That is to say, the dynamic buckling modes given by the Twin-characteristic-parameter solution are also the preferred mode of buckling. Calculation results shows that the first order of the critical load of dynamic buckling is much higher than the static critical load with the same boundary condition. So the transverse inertia should be considered in the calculation of the critical load of dynamic buckling.