In designing a bolted joint, it is important to estimate an increment in axial bolt force when an external tensile load is applied to an assembly. The ratio of the increment Ft in the axial bolt force to the external tensile load W is called the load factor φ(=Ft/w). The formula φ=K t/(Kt+Kc) proposed by Thum has been applied for estimating the value of the load factor φ, where Kt is the spring constant of bolt-nut system and Kc is the compressive spring constant of clamped parts. It has been found that the value of the load factor varies with the position of load application to the assembly. Then, a method to compensate Thum's formula was proposed. However, this compensation is made empirically and the theoretical background is not made clear. In this paper, the concept of the tensile spring constant Kpt for clamped parts is introduced newly when an external load is applied to the outer circumference of clamped parts (hollow cylinders) and a method for estimating the value of the load factor exactly is proposed by using Kpt. The value of Kpt is analyzed using an axisymmetric theory of elasticity. For verification of the proposed method, experiments were carried out to measure the load factor. A fairly good agreement is seen between the analytical and the experimental results of the values of the load factor while the values of the load factor obtained from Thum's formula were so different with the experimental results. The reason why the difference in the values of the load factor is substantial between values and the values obtained from Thum's formula is elucidated. It is found that the value of the load factor decreases as the outer diameter of the hollow cylinder increases and the as thickness of the clamped parts decreases. In addition, FEM calculations for the load factor are carried out. The FEM results are in a fairly good agreement with the theoretical results.