A bag having both a support system and a closure system is provided. The closure system of the bag provides structural support to the bag. In at least one embodiment, the bag includes at least one sheet of flexible material assembled to form a semi-enclosed container, an opening within the semi-enclosed container defined by a generally circular periphery of the semi-enclosed container at an unenclosed end of the at least one sheet of flexible material, and a flexible support rim disposed around the generally circular periphery of the semi-enclosed container at an unenclosed end. The support rim is sufficient to support the opening within the semi-enclosed container in an open position.