The stresses of joints combining the bonding force of adhesives with the clamping force of bolts is analyzed using axisymmetrical theory of elasticity and FEM, when an internal pressure is applied to the combination joint in which two pipe flanges are clamped together by bolts and nuts with an initial clamping force after being joined by anaerobic sealant. The anaerobic sealant is applied at the interfaces partially instead of formed gaskets in pipe flange connections. In the numerical calculations, the effect of the bonding area and position and Young's modulus of sealant on the contact stress at the interfaces are clarified. In addition, using the interface stress distribution, the strength of the combination joint is predicted. Experiments were performed and the analytical results are consistent with the experimental results concerning the variation in axial bolt force and the strength of combination joints. It is found that the joint strength changes as the bolt pitch circle diameter, the bonding position and its area, the initial clamping force and the adhesive material properties change. Furthermore, it is seen that the sealing performance of such combination joints in which the interfaces are bonded partially is improved over that of pipe flange connection with metallic gaskets.