Taking the leakage of steel pipe welding neck flanges with raised face as the research object, the thickness of the fixture calculated from the two formulas of the torque-less film theory and the bending beam deformation theory is compared with the thickness of the fixture used in the actual application and the mechanical properties of the three different thickness fixtures were analyzed by using the finite element software Abaqus. The results show that the thickness of the fixture calculated by using the torque-free thin film theory is far away from the thickness of the actual fixture. The thickness of the fixture calculated by using the bending beam deformation theory is almost the same as the actual fixture thickness, which is more suitable for practical applications. The design thickness of the fixture plays an important role in the precision and service life of the fixture. Therefore, the theoretical calculation formula of the fixture strength needs further improvement and research.