A suture assembly includes an elongated flexible body which may be either a singlefilament for a multiple strand braided or woven body, supporting a pluralityof 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 whilea straight pointed body is joined to the remaining end of the flexible body. Inalternate embodiments, the tissue-engaging elements define a variety of cross-sectionshapes. In a further alternate embodiment, the tissue-engaging elements aredivided into first and second oppositely facing sets to provide a bidirectionalsuture. In a still further alternate embodiment, the elongated flexible bodysupports an elongated tissue- bonding sleeve.