A suture anchoring system having an anchor structure through which at least one suture can extend, the anchor being compressible or deformable to anchor the suture, and a method for using the suture anchoring system by attaching one end of a suture to a muscle, ligament or bone; threading the suture through an osteal tunnel; providing a surgical anchor comprising a cuff of deformable material suitably shaped to receive a suture, wherein said cuff, when compressed, tightly grips a suture and forms a point of support, whereby said deformed anchor prevents a suture from being pulled through a drilled osteal tunnel; threading the other end of the suture through the anchor; and deforming said anchor tightly about the suture to form a point of support.