Elements (5) such as dental fillings, inlays, dental veneers, root pins, implants to be implanted in bone tissue, or endoprostheses are affixed to surfaces (3) of dentine, tooth enamel, bone tissue, or a corresponding substitute material, by providing the element with element surfaces (6) including a first thermoplastic material, by equipping the surfaces (3) of dentine, tooth enamel, bone tissue, or a corresponding substitute material in a preparatory step in such a way that they become weldable with the first thermoplastic material, and by welding the element surfaces (6) to the pre-treated surfaces (3) by e.g. exciting the appropriately positioned element (5) with mechanical vibrations. The pre-treatment of the surfaces (3) in the preparatory step is achieved by attaching solid bodies (2) including a second thermoplastic material to the surfaces (3), with the aid of a curable compound (generally known for preparatory treatment of dentine or enamel surfaces) or with the aid of a cement.