Pipelines play a dominant role in the transportation of oil and gas and the safety of pipelines is essential for the supply of energy. However, natural disasters such as floods and land subsidence may lead to suspended pipelines, resulting in pipeline failure accidents, causing casualties and environmental pollution. To deal with the emergency caused by suspended pipelines, it is needed to identify the failure mechanisms of suspended pipelines caused by natural disasters. Therefore, this study conducts a safety analysis of suspended pipelines using a nonlinear finite element method (FEM), considering the nonlinear pipe–soil contact and plastic deformation. A case study is conducted to investigate the influencing parameters (e.g., the suspended length, the operating pressure, and the fluid mass). This work demonstrates that irreversible plastic strains occur when the suspended length exceeds 50 m, and it will reach 2% when the suspended length is 340 m. Finally, an emergency response plan based on plastic strain and suspended length is proposed to determine the emergency level of the suspended pipelines caused by natural disasters. This study can provide technical support for the emergency response of pipelines in areas with frequent natural disasters, promoting the sustainable development of oil and natural gas pipelines.