Objects are fastened to object surfaces of a porous or fibrous material, in particular made of wood or a wood-like material, with the aid of a thermoplastic fastening film. For this, the object, which is separate from, or integrated in the fastening film, is positioned on the object surface and, with the aid of a vibrating fastening tool having a distally arranged, for example closed, perimetric profile element, which is positioned on the fastening film, is anchored in the object surface along a perimeter, and optionally also punched out. The fastening is suitable in particular for fastening identification carriers to wooden objects such as pallets or tree trunks, wherein the identification carriers are equipped, for example, with an antenna and an RFID chip or with a bar code.