A flexible, elongated suture passing device or shuttle capable of advancing monofilament or multi-stranded suture material to a remote work site. The suture shuttle is formed of a plurality of woven or braided fiber strands which are coated, over all but a central portion of the strands, with a material having a flexible exterior surface. A part of the central portion of the strands is formed into an eyelet for receiving a suture therethrough. A method is disclosed wherein one end of the suture shuttle is advanced to a work site until the eyelet passes through the tissue at the work site. This enables suture to be passed through the eyelet so the shuttle may be withdrawn to pass the suture back through the tissue to be sutured. Repeating this process brings any desired number of suture leads through the tissue so a knot may be tied.