Assembly drum of variable diameter D, intended for the manufacture of a tire blank, the drum having a generally cylindrical laying surface (2) provided with circular grooves (3) arranged axially in a zone intended to receive profiled elements of great thickness, said groove (3) containing elastic circumferential bodies (4). When the drum D is moved to a first laying diameter, a mechanical means moves the elastic body (4) radially apart from the bottom of the groove, so as to align the radially outer surface of the elastic body (4) with the laying surface of the drum (2).