Abstract:In the present paper,the free vibration of beam of materials of linear kinematical hardening was investigated.The results showed that the natural frequency has changed with the plastic deformation,and it was below the natural frequency of elastic vibration of the beam.It was also shown that the frequency of the first vibration was the smallest one;the later frequency of vibration was gradually increased by the plastic deformation and kinematical hardening,until the vibration was elastic.In this case,the natural frequency was the elastic one,and the strength of vibration keeps unchanged.