Abstract: The finite element character-value method is used to study the dynamic buckling of bars under elastic compression wave. The finite element characteristic equations are derived based on the adjacent-equilibrium criterion. In these equations, the compression wave propagation and the transverse inertia effect are taken into consideration. By using the dynamic buckling supplementary restraint conditions at the compression wave front of bars at the instant of buckling, the critical-load and dynamic buckling modes of bars are calculated from the solutions of the finite element characteristic equations.