A stapling element is provided, operative to pierce and penetrate a tissue by a first end, and close around the tissue. Three factors help prevent local necrosis: 1. The self-closing feature of the staple does not lead to tissue crushing. 2. Edge seams are applied generally perpendicular to the tissue edge, allowing for blood supply to the tissue edge. 3. Excess tissue is cut off at the seam, minimizing the amount of tissue that may undergo local necrosis. A physical feature prevents the staple from rotating, when in an application shaft, to maintain a predetermined closing direction. The stapling element may be formed of an alloy, a pure metal, a polymer, or a composite of at least two materials. Additionally, staplers, anastomosis devices, and methods for their applications are described.