An apparatus for forming objects, in particular containers, and for applying respective labels thereto, includes a forming arrangement provided with a punch cooperating with a cavity of a die to make the objects by forming a sheet of thermoformable material. The cavity includes a first wall element and second walls. The first wall element is movable between a first operating position in which it receives a label and a second operating position in which it bounds the cavity in cooperation with the second walls, and supports the label in such a manner that during a subsequent forming operation the label is fixed to, in particular substantially incorporated in, the object.