This paper investigates the class of weak models of the calculi RCC-5 and RCC-8, which are basically first-order models of the theories specified by the composition table. We show that simple structures, viz. sets and general topological spaces provide natural weak models. Conversely, we prove that for any finite weak model there are finite structures upon which the model is based. We interpret the construction of the models described by Renz as lifting those finite models to models in the Euclidean space.