Before this study, no analytical models had been made available for describing the behaviour of plane geostructures subjected to thermal and mechanical actions. This knowledge gap notably represented a limitation for investigations about the behaviour of so-called energy geostructures, which are subjected to the considered actions due to their geothermal heat exchanger and structural support roles. In this study, the first analytical model that allows describing the behaviour of plane geostructures subjected to thermal and mechanical actions is presented. This model extends Winkler’s solution to non-isothermal conditions for quantifying the effects of temperature variations, axial loads, transversal loads and bending moments applied to plane geostructures resting on an elastic soil mass. The model is applied to the analysis of an elementary unit represented by a single beam as well as to more complex plane geostructures using the superposition principle. The obtained results are compared with predictions deriving from more rigorous yet time-consuming numerical analyses, showing close agreement. This result makes the developed analytical model a useful tool for scientific and engineering purposes, paving the way for future developments in this scope.