A package for a number of beverage or non-beverage containers includes an overlay member covering the top or bottom ends of the containers. The overlay member has a central, generally planar panel positioned on the ends of the containers and may include a number of perimeter panels each joined to and positioned on a perimeter of the central panel. Each perimeter panel is oriented generally perpendicularly relative to the central panel. A dispenser opening is in the central panel of the overlay member through which the containers may be removed from the package. An overwrap member such as a thermoplastic shrink wrap film envelops the array of containers and the overlay member to provide a robust, unitary package for transport and storage. A line of weakness in the overwrap member is aligned with the dispenser to allow a user to puncture the overwrap member in the vicinity of the line of weakness and gain access to the containers via the dispenser. The package may be supported on a shelf such as within a refrigerator or storage rack with a side of the package facing downwardly and the dispenser positioned proximate the downwardly facing side of the package.