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Chilled gas pipelines buried through the boundary between permafrost and non-permafrost soil are subjected to serious deformation due to differential frost heave. In order to predict bending stress and strain of pipelines for engineering design, it is necessary to develop an adequate model for interactive behavior between frost heave and pipelines. This work presents a potential method based on beam on elastic foundation model, two-dimensional temperature distribution analysis, and Takashi s equation, in order to contribute the above-mentioned problem. The governing differential equation is solved analytically according to the boundary and continuity conditions. Spring coefficient and distributed loads in permafrost and non-permafrost soils are the main parameters controlling elastic response for a beam on elastic foundation. Those parameters are revised in the frame of pipeline deformation induced by frost heave and appropriate parameter assumptions are proposed in this study.