With the help of modeling by ANSYS and application of finite element method, 3D static analysis of GIS pipe shell, the self-vibration analysis of the whole structure are carried out in this thesis. The basic principles of modal analysis in ANSYS are introduced. After establishing the integral finite element modal considering the self-weight of GIS pipe shell in ANSYS, the structural model analysis is carried, the top 30 order models are obtained, and the former five-order vibration mode are listed in this thesis. The analysis about the free vibration characters of the GIS pipe shell structure shows that the lateral stiffness in two direction of the structure is relatively uniform, and the structure is comparatively regular, with small torsional rigidity. Also it suggests that the stiffness of side force resistance and torsion resisting stiffness should be improved during the design process.