A suture anchor includes a body having a distal end and a proximal end. Projections in the form of ribs or threads are formed on the body for retaining the anchor in a hole formed in bone. An eyelet formed on the distal end of the body accepts suture. The eyelet preferably is formed by a loop of suture. Where the body of the anchor is formed of a polymer, the suture loop can be formed by insert-molding the suture into the body. Tissue is reattached to bone using the suture anchor by securing a length of suture to the tissue, and threading the length of suture through the eyelet on the distal end of the anchor, leaving lengths of suture extending from either side of the eyelet. Installing the suture anchor into the bone wedges the lengths of suture between the suture anchor and the bone, thereby securing the tissue without the need for tying knots. Pullout strength can be enhanced by twisting the lengths of suture prior to installation of the anchor into the bone.