A suture assembly includes an elongated flexible body supporting a plurality of frusto-conically shaped tissue-engaging elements in a generally spaced arrangement thereon. A curved body having a sharp point is joined to one end of the flexible body while a straight pointed body is joined to the remaining end of the flexible body. In alternate embodiments, the tissue-engaging elements are elliptical or polygonal in cross-section. In a still further alternate embodiment, the tissue-engaging elements are divided into first and second oppositely facing sets to provide a bidirectional suture.