Large-diameter buried pipelines are widely used because of their energy-saving advantage and high efficiency. In this study, an “L”-type heat pipe network was considered as research object and studied using flow–heat–solid coupling method. The ANSYS Workbench platform was used to simulate heat transfer and medium flow in the pipe network. The maximum equivalent stress and deformation of the pipe network under different displacement release conditions were calculated and compared with those under no-displacement release condition. The displacement release of the end sides did not change the stress and deformation distribution of the entire pipe network system but reduced the maximum equivalent stress and deformation, resulting in improved safety and stability of the pipeline. When the total amount of the displacement release of the inlet and outlet sections was defined, the influence of unequal end-side displacement on the stress and stress distribution of the pipe network can be neglected. Moreover, the maximum deformation gradually decreased with increasing displacement release in the inlet section and rapidly decreased with increasing total displacement release amount.