The dynamical behaviours of a simply support buckled beam under axial harmonic excitation are investigated using the direct numerical method,and the effect of rotary inertia is considered too.The governed equation of buckled beam is transformed to the nonlinear partial differential equations of physical variables such as moment,velocity and displacement.By using a stable,explicit finite difference scheme to solve the equations and the solutions is equivalent to the Galerkiin solutions.Various complex dynamical behaviours such as period doubling,quasi periodic and chaotic motion in this system are shown,and the result also demonstrated that the finite difference method is more convenient than other tradition methods for the study of buckled beams.