One of the main problems of well operation is the risk of uncontrolled leakage of hydrocarbons into the environment. This problem is especially relevant for the long-term operation of wells. The idea for this study was inspired by a real industrial problem that the authors of the article were involved in solving. At several operating gas wells, an abnormal slope of the production tree occurred, which raised the question of the safety of their further operation. An analysis of known studies and current regulatory documents did not allow us to assess the safety of using a gas well based on the measured kinematic parameters of production tree deviations. A mathematical model for the deformation of a package of casing strings when the surface layer of the rock is displaced is developed in the article. A boundary value problem is formulated for differential equations of pipe bending on an elastic foundation. Based on the results of solving this problem, an unambiguous relationship was established between the maximum bending stress in the surface pipe and the angle of inclination of the production tree. The quantitative characteristics of the connection depend on the geometric and mechanical properties of the pipes and on the thickness and mechanical parameters of the formations. It was established that the existing inclination of the production tree can be achieved due to the beginning of the plastic bending of the surface pipe under the slickenside, which does not exclude the exhaustion of the safety margin of the surface pipe and indicates the possible operation of the casing string in a pre-emergency state. In general, the obtained results develop analytical approaches to assessing the behavior of underground structures of a production well in unstable soil bodies.