The subject of this paper is an analysis of the influence of circumferential prestressing on the interaction of cylindrical silos and tanks with the subsoil. The behaviour of the shell structures of RC and PC cylindrical silos or tanks (with circumferential pre-tensioning), and particularly of the ground slab interacting with subsoil, depends largely on the function graphs of the subsoil reactions on the foundation surface. Distributions of the subbase reactions on the ground slab in such structures as silos and tanks have a significant impact on the behaviour of not only the slab itself, but also the interacting shell structure. An analysis of these structures with walls fixed in a circular ground slab and foundation ring was carried out taking into consideration the elastic half-space model using the Gorbunov-Posadov approach and the two-parameter Winkler model. In the computational examples of RC and PC silos and tanks with walls fixed in the circular ground slab or foundation ring, the eventual effects of prestressing obtained as a result of the superposition of internal forces were examined. Although the results for both subsoil models proved to be divergent, the conclusions that follow are fairly important for the engineering practice.