The construction of urban subways and underground passages inevitably involves undercrossing existing municipal pipelines, which can cause pipe deflection and threaten pipeline safety. Most of the existing prediction theories for pipeline deformation caused by tunneling use elastic foundation models such as the Winkler model and the Pasternak model, which lack consideration of the nonlinear interaction between soil and pipelines. To further consider the nonlinear deformation of the soil, a simplified calculation method for predicting the nonlinear deformation of pipelines caused by tunneling was proposed. Firstly, a nonlinear foundation model was introduced, and the existing municipal pipeline with rigid joints was regarded as a continuous beam on the nonlinear foundation. Secondly, the ground displacement at the axis of the pipeline caused by single-line and double-line tunneling was calculated respectively, using the Peck empirical formula and the modified Peck empirical formula that considers the tunnel construction sequence. Then, assuming that the pipeline and soil deformation are coordinated, the differential control equation for pipeline deformation caused by tunneling was established, and the deformation solution of the pipeline was obtained using finite difference method and Newton iteration method. Finally, the rationality and applicability of the proposed method were verified by comparing its results with monitoring data from a centrifuge experiment and two engineering cases. The results show that the proposed method can effectively predict the longitudinal deformation of existing municipal pipelines with rigid joints caused by tunneling well in both sandy and clayey soil layers. It can also predict the pipeline deformation caused by twin-tunnel undercrossing after considering the effect of tunnel construction sequence. Compared with other foundation models such as the Winkler foundation, Pasternak foundation, and Kerr foundation, the proposed method has a better agreement trend with the measured data. This research provides a new prediction method for predicting the deformation response of municipal pipelines caused by tunneling and can provide theoretical support for the safety assessment and deformation prediction of municipal pipelines.