Abstract: On the basis of the dynamic stability character analyses of elastic bars subjected to axial compression, the theoretical analyses of dynamic buckling for the bar with two end fixed and the bar with one end hinged and another end fixed are performed. Expanding the characteristic equations with double parameters, the dynamical buckling critical loads and the buckling modes of two different boundary conditions are achieved. It is demonstrated that the solution of mode function is not the bar’s buckling solution when . Furthermore, some other respects about the stress-wave-induced buckling are discussed and the result is very consistent with that of experimental studies