The lining rings of a shield tunnel are connected by steel bolts, which play an important role in longitudinal structural deformation during long-term operation. In recent decades, there have been increasing numbers of tunnel-crossing projects. In order to better understand the impact of undercrossing excavations on existing tunnels and to provide a quick and effective tool for evaluating the behaviors of existing tunnels before construction, a simplified analytical method is proposed. In the proposed model, a tunnel was simplified into a series of short beams connected by shear, tensile, and compressive springs, and the Pasternak two-parameter foundation model was used to describe the tunnel–soil interaction. The tunnel model not only considers the shear effect between the linings but also the rotation effect of the lining ring. The field data from two cases were used to compare with the calculated results, and the predictions were found to be in good agreement with the measured data, thus verifying the effectiveness of the method.