Today, pipelines are the safest and most economical way to transport petroleum products and one of the key components of modern energy infrastructure. Nevertheless, pipeline systems are associated with certain risks that can lead to environmental disasters. The idea of carrying out this study was initiated by the results of the survey of the overpasses of the long-used oil pipelines laid in the mountainous area of the Carpathian region. Defects such as a change in the shape of the pipe and local bulges in the area of oil pipeline support nodes were detected. The explanation of the described problem is separate from the typical algorithms of design calculations, which are offered to manufacturers by current directive documents. The desire to provide an explanation and quantitative assessment of the detected defects became the main motivation for writing the article. An analytical model of the interaction of the oil pipeline with the rigid support has been developed. Additional internal loads in the cross-section of the pipe and displacement of its middle surface, which arise as a result of such interaction, are determined. The method of determining the reaction in the intermediate support of the overpass of the oil pipeline has been developed, considering the properties of the soil base in the underground sections and the mounting gap in the support node. The analytical dependence was obtained to determine the additional hoop stresses that arise in the oil pipeline due to the contact of the pipe with the support. The unambiguous relationship between the maximum additional hoop stress and the reaction in the support node was established. The dependence of additional hoop stresses on the geometric characteristics of the pipes was analyzed. The obtained research results are tested on the real structure of the overpass of the Druzhba oil pipeline, built in the Carpathians. In general, a simple engineering technique has been developed that allows analyzing the behavior of the oil pipeline support node and provides the numerical correction to the traditional strength assessment formulas, which determine the equivalent stresses in the oil pipeline.