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 a raised member made of flexible, rubber-like material, having at least one opening through which wipes are removed when the lid is open. When the lid is closed it compresses the raised member. When the lid is released from its closed position the raised member pushes the lid open. The dispensing means may have a hard plastic backing member underneath a portion of the rubber-like material adjacent the opening through which wipes are removed.