In order to establish dynamics equation of resonator in HRG,the strains and stresses of an arbitrary point in the hemispherical thin shell were deduced under Kirchhoff-Lyav hypothesis.The force and torque equilibrium equations of the thin shell element selected from the resonator were gained on the basis of the calculated strains and stresses,then the border motion equations of the HRG were obtained in consideration of the subjected 3-D angular rate and the 3-D angular acceleration.Finally the dynamics equations of resonator were established by Bubonov-Galerkin method which is common used for solving differential equations,thus the natural frequency is computed by the established dynamics equations.By contrast with other methods of calculating natural frequency and the measured frequency values of practical HRG,the correctness of the established dynamics equations and the method of frequency calculation are proved.