Abstract: In order to form positive connections with human or animal tissue parts, particularly bones, implants (7) are used that at least partially consist of a material that can be liquefied by means of mechanical energy. Particularly suitable materials of this type are thermoplastics (e.g. resorbable thermoplastics) or thixotropic materials. The implants (7) are brought into contact with the tissue part, are subjected to the action of ultrasonic energy and are simultaneously pressed against the tissue part. The liquefiable material then liquefies and is pressed into openings or surface asperities of the tissue part so that, once solidified, it is positively joined thereto. The implantation involves the use of an implantation device comprising a generator (2), an oscillating element and a resonator (6), whereby the generator (2) causes the oscillating element to mechanically oscillate, and the element transmits the oscillations to the resonator (6).