A container for wipes, and a cap for the container, having a pop-up style dispensing means positioned beneath a reclosable lid. The container may be as upright cylindrical container for perforated wipes or a rigid tub for interfolded wipes. The dispensing means comprises flexible, rubber-like material having at least one opening through which wipes are removed from the container when the lid is open, and a hard plastic backing member underneath a portion of the rubber-like material adjacent the opening through which wipes are removed.