In the condition of engineering surcharge near the existing pipeline, the pipeline will produce subsidence deformation and further the normal operation of the existing pipeline will be threatened. Most of the research in this area stays in the finite element and indoor tests, and few theoretical solutions are used to analyze the stress and deformation response of existing pipelines under adjacent engineering surcharge. Based on this, this paper investigates the pipeline-soil interaction under this working condition by using theoretical analysis. Firstly, the Boussinesq solution is used to analyze the additional stress at the axis of the existing pipeline. Then, the pipeline is simplified as an infinite beam rest on the Pasternak model to further obtain the total energy of the system during the deformation of the pipeline. Finally, the stress and deformation response of the pipeline can be obtained according to the energy variation theory. By comparing with the existing experimental data, the correctness of the proposed method is verified. Compared with the degradation analysis of the proposed method, the proposed method is closer to the measurements. The parameter study shows that the stress deformation of the pipeline will decrease nonlinearly with the increase of the buried depth of the pipeline. Increasing the diameter of the pipeline will increase the deformation response of the pipeline, the deformation of the pipeline is not sensitive to the angle between the pipeline and the loading area. Increasing the horizontal distance between the pipeline and the loading area can effectively reduce the stress and deformation response of the pipeline, and the deceleration increases first and then decreases. A series of analysis results can be used to analyze the influence of engineering surcharge on the stress and deformation of existing pipelines in practical engineering.