In the paper, the eigenfrequencies of a hemispherical resonator of the Coriolis vibratory gyroscope have been studied by the finite element method (FEM) using ANSYS Mechanical. Consideration was given to the feasibility of various FE used in the ANSYS to solve the problem of determining the eigenfrequencies. The specifics of working with shell and solid-state elements were established. The results of analytical and numerical solutions of the mentioned problem were compared. The presence of «mathematical» frequency split caused by the used FEM and the unsymmetrical mesh of the FEM was noted, and the need to take this split into account when introducing the defect distribution function into the model was pointed out. The technique for finding the frequency split value resulted by added defect in the presence of «mathematical» frequency split component was demonstrated.