A method for joining two objects by anchoring an insert portion provided on one of the objects in an opening provided on the other one of the objects. The anchorage is achieved by liquefaction of a thermoplastic material and interpenetration of the liquefied material and a penetrable material, the two materials being arranged on opposite surfaces of the insert portion and the wall of the opening. Before such liquefaction and interpenetration, an interference fit is established in which such opposite surfaces are pressed against each other, and, for the anchoring, mechanical vibration energy and possibly a shearing force are applied, wherein the shearing force puts a shear stress on the interference fit.