The accumulated water in the cavity behind the tunnel lining in cold regions may freeze under low-temperature conditions, resulting in local frost heave pressure. Assuming that the cavity behind the tunnel lining was a semi-elliptical space, the interaction between the surrounding rock, ice body, and lining during the frost heave process was simplified as springs in series, and an analytical solution for the local frost heave pressure in the semi-elliptical water-accumulated space was proposed. A three-dimensional numerical model was developed to verify the effectiveness of the analytical solution. Further, the relationships between local water-accumulated frost heave pressure and surrounding rock grade, lining stiffness, water-accumulated depth, and frost heave level were studied, and the influences of frost heave position on the mechanical characteristics of lining structure were analyzed. The results show that the local water-accumulated frost heave pressure of the cold region tunnel is negatively correlated with the surrounding rock grade and positively correlated with the lining stiffness, water-accumulated depth, and frost heave level. The influence degree of various factors on frost heave pressure is as follows: water-accumulated depth > lining stiffness > surrounding rock grade > frost heave level. The impact of water-accumulated frost heave on the lining structure mainly occurs in the contact area between the ice body and the lining, leading to the convergence of the tunnel towards the inner side. The principal stress of the lining is maximum when the water-accumulated space is located at the inverted arch, and the principal stress of the lining is minimum when it is located at the arch foot. Under the action of local frost heave, there is a sudden change in the bending moment and axial force of the lining structure, manifested as the bending moment increase and axial force decrease of the lining under tension on the air side, as well as the bending moment decrease and axial force decrease of the lining under tension on the surrounding rock side. The stiffness differences in different zones of the lining lead to different impacts of frost heave pressure on structure safety. The influence degree of frost heave position on structure safety is as follows: vault > inverted arch > arch shoulder > arch foot > wall foot.