Implants for forming a positive connection with human or animal parts include a material, such as thermoplastics and thixotropic materials, that can be liquefied by means of mechanical energy. The implants are brought into contact with the tissue part, are subjected to the action of ultrasonic energy while being pressed against the tissue part. The liquefiable material liquefies and is pressed into openings or surface asperities of the tissue part so that, once solidified, the implant is positively joined thereto. The implantation involves the use of an implantation device that includes a generator, an oscillating element, and a resonator. The generator causes the oscillating element to mechanically oscillate, and the element transmits the oscillations to the resonator. The resonator is used to press the implant against the tissue part to transmit oscillations to the implant.