A tie bag for storing refuse or garbage includes an undulating top edge defining an opening to the bag. The top edge may include two flaps and two valleys. In one embodiment, the valley may include a flat portion at the bottom of the valley. The flaps may be tied together to at least partially close the bag. The bag further may include a first seam that intersects the flat portion of the valley. The flat portion reduces the possibility of tearing the seam. In another embodiment, the valley may include a slit. In an additional embodiment, the valley may include two secondary valleys and a center valley. In another embodiment, the seam may intersect the top edge at a point other than the lowest point in the valley.