Abstract: The nonlinear dynamics equation of a equal section beam under pure bending vibration was developed . According to theory of the nonlinear dynamics, the singular point and stability of the system was studied. Using theory of Chaos, the parameter condition of a equal section beam for occurred Chaos under pure bending vibration was explored. According to the parameter condition , the parameter condition of a equal section simply supported beam for occurred Chaos under pure bending vibration was studied., the parameter dividing line of occurred Chaos were obtained.