An anastomosis is performed using a flexible mounting structure mounted on the outside of at least one vessel. Fasteners extend through the vessel and are bent towards the incision to attach the flexible mounting structure to the vessel in a manner that controls the edge of the vessel adjacent to the incision. The mounting structures are oriented on each vessel so fasteners on one mounting structure interdigitate with fasteners on the other mounting structure at the location of contact between the vessels when the two vessels are brought together. This creates two complementary sinusoidal-shaped vessel edges with peaks of one edge being accommodated in the valleys of the other edge. The peak-to-valley orientation forms a sinusoidal-shaped joint which is leak free. The fasteners are spaced so proper pressure is applied to the tissue to promote healing without leaking. Furthermore, the fasteners are sized and shaped to properly engage the tissue and bend in a desired manner. Methods and tools for carrying out the anastomosis according to the invention are also disclosed. Methods for forming the fastener and the tines having the proper characteristics are disclosed. An absorbable ring-shaped stent is also disclosed.