Three-dimensional finite element method analysis on the tunnel-soil-underground pipeline was carried out based on the ABAQUS program. PSI element was applied to simulate the interaction between the pipelines and soil. Parameters such as an elastic modulus of soil, stress release rate, at-rest lateral pressure coefficients, an elastic modulus of pipelines, and buried depths of tunnels were analyzed. The effects of tunnel excavation on the displacement of existing pipelines were investigated, and the settlement relationships were obtained. The relationship between each parameter and surface settlement was determined by the grey relational analysis method to analyze each parameter’s sensitivity to the settlement of the pipeline, which can provide a reference for emphasis and methods of shield tunneling support. Finally, a formula of the settlement relationship between the maximum surface settlement and pipelines deformation was proposed for different pipe-soil relative stiffness. The formula was applied in the practical case. Compared with the field monitoring results and FEM computer results, it has been found that the proposed normalized formula is consistent with the measured results and numerical simulation of the pipeline settlement.