Under the special geological environment of the buried pipe, the ground is lost at the bottom of the pipe, which is created by various kinds of external factors. The pipe in the suspended state would be greatly deformed due to its own weight, internal pressure, and other factors, resulting in the failure of the pipeline. When a variable wall thickness weld occurs in the suspended section of the pipeline, the change of the pipeline stress will be more complicated and changeable. In this study, ABAQUS software is used to establish a pipe–soil model of variable wall thickness butt welds of suspended pipelines. The axial stress distribution with different affected factors in the pipe, the change of curvature, and Mises stress change of the entire pipe along the axial direction are obtained by analyzing the internal pressure, wall thickness ratio, suspended length, weld position, and cone length. The results show that the stress at the root of the weld changes significantly; therefore, the weld has a greater impact on the stress of the entire pipeline. The change of internal pressure has little effect on the stress at the pipe weld. As the suspended length increases, the change in stress at the weld is more obvious. When the weld seam is close to the soil, the support of the soil will gradually shift the maximum stress position of the pipe from the top of the pipe to the bottom of the pipe. With the increase in cone length, it will reduce the sudden change of pipe section and the change in stress effectively. The places where the curvature greatly changes along the axial direction are at the pipe–soil separation and the middle of the pipeline, while the stress reaches the maximum at the pipe–soil separation, and the place with the largest stress change is the weld in the middle of the pipeline.