Abstract: Elastic supports are recognized as an efficient means for structural designs under thermo-mechanical loads. Their introduction is beneficial not only for the achievement of the specific structure stiffness but also for the reduction of stress intensities to match the thermal deformation of the structure. In this paper, both theoretical and numerical studies are carried out to optimize the elastic support under thermo-mechanical loads. First, the analytical expression of the maximal thermo-mechanical stress is derived for a beam model with elastic support to illustrate the effects of the load-bearing and thermal deformation coordination of the elastic support. On this basis, a general topology optimization model and related topology optimization methods are proposed. Numerical examples and results are presented to demonstrate the validity of the proposed approach.