The invention deals with the method and apparatus for forming sutures utilizing ultrasonic vibrational energy as well as the sutures formed thereby. The sutures are formed in biological organisms, such as humans, in a manner to substantially eliminate the loosening of the suture after its formation. In one form of the invention, tie offs in the form of knots as presently practiced are eliminated and overlapping portions of the suture are ultrasonically bonded or welded together without first forming a knot. In another form of the invention the ultrasonic vibrational energy is applied to the knot portion of the suture to prevent slippage and loosening thereof as stresses are applied thereto by normal body movement or in particular by the muscular system. The ultrasonic mechanical vibrations are applied to thermoplastic suture materials that are in either the plastic or metallic family, or of a natural or synthetic polymeric material.