A low profile beverage container holder having a base support for supporting the beverage container and a wall which extends around the base and thereby defines a cavity for receiving the beverage container. The holder is also provided with a wedging structure. In the preferred embodiment, the wedging structure comprises an annular rib disposed in the cavity and projecting upwards from the base support. Thus, when the beverage container is tipped, the annular rib contacts the concavity on the bottom surface of the beverage container and the container is thereby wedged between the annular rib and the low sidewall. A plurality of beverage containers which are adapted to be received within the beverage container holder are also disclosed.