A first and a second object (1 and 2) are joined with the aid of a joining element (8) comprising at least in the region of its distal and proximal end (8.1 and 8.2) a thermoplastic material. Two blind holes (5 and 6) facing each other are provided in the two objects (1 and 2) and the joining element (8) is positioned in the blind holes such that its distal and proximal ends (8.1) are in contact with the bottom faces of the blind holes and such that there is a gap (9) between the two objects (1 and 2). This assembly is then positioned between a support (3) and a sonotrode (4). The sonotrode (4) and the support (3) are forced towards each other, while the sonotrode (4) is vibrated, thereby liquefying at least part of the material having thermoplastic properties, there, where the joining element ends (8.1 and 8.2) are pressed against the bottom faces of the holes (5 and 6) and allowing the liquefied material to infiltrate into pores of the hole surfaces or unevennesses or openings provided in the hole surfaces, such anchoring the joining element ends (8.1 and 8.2) in the objects (1 and 2). For achieving suitably similar anchorage qualities at the two joining element ends (8.1 and 8.2), the distal end (8.1) of the joining element (8) has a smaller face area and comprises less thermoplastic material than the proximal end (8.2) of the joining element.