This review article is divided into three parts. Firstly, three soil/structure interaction problems are described in which strain is imposed on the soil caused by solar heating of the structures. They are modeled by reference to cyclic ratcheting strains with the help of a simple two-component model comprised of one elastic element and one element of granular material. Possible stable shakedown solutions are described for a bridge and filter bed. In contrast, a tower structure may become progressively less stable with increasing load cycles. Secondly, our experimental results from plane strain biaxial tests on sand under drained cyclic loading conditions are shown to complement the work of others. Results reveal the existence, in strain control experiments, of a unique shakedown stress ratio, S, which is independent of cyclic strain amplitude, but with the associated void ratios being strain-amplitude dependent. At very small strain amplitudes S may decrease. Thirdly, numerical modeling methods are described. These include applications of nonlinear elasticity, and elasto-plasticity including endochronic theory, to predict the behavior of granular materials under cyclic loading. It is concluded that temperature-induced cyclic loadings are of importance in some soil/structure interaction situations, and that reliable predictions can be made in simple cases. Further knowledge and research is needed to fully predict the incremental evolution of fabric change during cyclic stressing and cyclic straining. Either existing models will be required to be modified, or new ones formulated to capture all the features covered in this paper. There are 51 references included with this article.