Both vibration and noise of gear system is more and more serious in the high speed and heavy gear transmission. Many researchers have conducted much study for them. But most of studies are on the torsion vibration of gear or the sound radiation characteristic of gear box, and fewer studies are on the structural bending vibration that occupies most of gear noise. Ordinarily, the vibration of gear structure is analyzed by using the theory of thin plate. However, the real gear is possessed of larger thickness. It is necessary to consider the effect of shear and bending deformations for investigating the compound vibration of gear body. This paper considers the gear structure as a midde thick plate. Its vibration differential equation about the elastic dynamics has been set up, and the natural characteristic of the gear has been studied. These provide the theorectic basis for investigating the noisy radiation characteristic of gear transmission system.