A supporting structure for concurrently holding a plurality of cylindrical containers for substances for medical, pharmaceutical or cosmetic applications is provided. The supporting structure includes a supporting base having a plurality of receptacles, which are configured such that the containers can be inserted into the associated receptacles, wherein the receptacles extend in the longitudinal direction of the containers and are configured to hold side wall portions of the containers at least partially clamped. The receptacles are continuous side walls, wherein the opening widths of the receptacles can be adjusted by a coordinated adjustment of the side walls of the receptacles between a first position, in which the containers can be inserted into the receptacles, and a second position in which the containers are clamped. The bottoms or upper ends of the containers are exactly fixed at a given height despite tolerances.