Abstract: The longitudinal axial force and the yield of joint bolts can result in significant nonlinear variations in the rotational stiffness of circumferential joints of shield tunnels subjected to external loading. The existing computational methods related to longitudinal deformation of tunnels often simplify the tunnels as an equivalent continuous long beam with the constant bending stiffness, which are challenging to reflect the nonlinear rotational effects of circumferential joints. Firstly, taking the transverse performance and elastic-plastic behaviors of bolts of a shield tunnel into account, the expressions for the rotational stiffness of joints under weak tensile bending, pure bending and compressive bending conditions are derived based on the strict elliptic parametric equation for cross-section of tunnels, respectively. Secondly, the shield tunnel is modeled as a series of Timoshenko short beams connected by nonlinear rotational springs and linear shear springs along its longitudinal direction, meanwhile the soil-tunnel interaction is simulated using the normal and tangential Winkler foundation springs, which are evenly distributed on the outer wall of the tunnel. Then, the state space method is used to obtain the longitudinal discontinuous displacement of the shield tunnel under external loads, and the iterative solution process associated with its longitudinal deformation under axial pressure is proposed. Finally, the proposed method is validated by comparing the existing theoretical methods and measurements associated with the upper excavation-induced longitudinal deformation of the tunnel, and the parametric analyses are also carried out to explore the impacts of longitudinal axial force and transverse performance on surface surcharge-induced longitudinal deformation of the tunnel using an engineering case. The results show that the yield of longitudinal bolts can significantly increase the joint opening and tensile area between adjacent rings. The application of axial pressure can prominently reduce the longitudinal displacement, joint opening and shearing dislocation of the shield tunnel induced by the upper excavation. The parametric analyses show that as the longitudinal axial force increases from tension to compression, the maximum longitudinal displacement and rotational angle of the tunnel decrease nonlinearly, and the decrease rate at first increases and then decreases, while the maximum joint opening diminishes approximately linearly. The reduction of lateral stiffness of the tunnel can lead to significant growth in its longitudinal displacement and joint opening, as well as a slight diminution in the shearing dislocation.