The construction of urban subways involves undercrossing existing municipal pipelines, which may threaten pipeline safety. Most of the existing prediction theories for pipeline deformation use elastic foundation models such as the Winkler model and the Pasternak model，which cannot account for the nonlinear deformation characteristics of soil. Therefore, an existing municipal pipeline with rigid joints was regarded as a continuous beam on a nonlinear foundation and a nonlinear deformation prediction method for pipelines was established. Firstly, the ground displacement along 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, the differential governing equation for pipeline deformation caused by tunneling was established, and the deformation solution of the pipeline was obtained using the finite difference method and the 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 is in better agreement with the measured data compared with other foundation models such as the Winkler model, Pasternak model, and Kerr model. It can also predict the pipeline deformation caused by twin-tunnel undercrossing while considering the effect of tunnel construction sequence.