As a chilled pipeline crosses a transition from frozen to unfrozen ground or shallow permafrost, a differential frost heave problem may develop causing strains in the pipe. Soil–structure interaction models that are currently available to handle this problem concentrate on the pipe as the dominant structural member and represent the soil mass as a series of unconnected springs. This paper considers the soil to be an elastic or nonlinear viscous continuum and imposes a nonlinear boundary condition to represent the frost heaving soil and the dependence of frost heave on applied pressure. The pipe is assumed to be a completely passive structural member and the soil strains at the pipe elevations are studied. The dependence of the maximum pipe strains on the length of the heaving section and on the thickness of frozen ground beneath the pipe have been established for a typical set of soil and frost heaving conditions. It is found that, for the conditions studied, when the thickness of shallow permafrost or frozen soil is greater than about 7–8 m, the strains that a flexible pipe experiences are less than the strain criteria currently in use on many pipeline projects.Keywords: frost heave, pipeline, interaction, stress analysis, finite elements, continuum mechanics, thermo-elasticity.