The invention relates to an osseous implant (10) that is implanted in a predetermined cavity or cavity that has been specifically produced, parallel to an implant axis (1) without a significant degree of rotation. Said implant has cutting edges (14), which do not lie on a common plane with the implant axis and are oriented towards the distal end of the implant. In addition, the implant comprises surface areas (16) consisting of a material that can be liquefied by means of mechanical vibrations. The cutting edges (14) are dimensioned in such a way that once implanted, they cut into the cavity wall. To carry out the implantation, said implant is subjected to mechanical vibrations, causing the thermoplastic material to liquefy at least partially and be pressed into uneven areas and pores of the cavity wall, where it hardens to form a connection between the implant (10) and the cavity wall by means of a positive fit and/or a union of materials. The cutting edges (14) provide anchorage for the implant in the cavity wall, in a similar manner to a screw-type implant. As the implant requires no rotation, the implant can have a form that is neither cylindrical nor conical and can thus be stabilised against rotative stresses more effectively than a screw-type implant. The implant is also more stable with regard to tensile forces as a result of the anchorage by means of the liquefiable material and can, in particular, be subjected to stress immediately after implantation. The implant is, for example, a dental implant.