The invention comprises a rotating transfer machine (40), arranged outside the path (P3) of the die cavities, having a plurality of transfer chambers (50) carried in continuous rotation, each adapted for containing a polymeric body (D) and for transferring it to a cavity of a die (21), and having means for moving the transfer chambers (50) along a same path (P2) so that this path (P2) has a portion (T1) overlapping with the path (P3) of the dies, during which each transfer chamber (50) is vertically aligned and synchronously moving above a corresponding cavity of a die (21), the transfer of the polymeric body (D) to the cavity of the die (21) being carried out in portion (T1). A relatively long path and thereby a correspondingly long time are provided for transferring polymeric bodies from the transfer chambers (50) to the die cavities, for carrying out and effective and correct transfer of the polymeric bodies into the die cavities, starting from a dispensing outlet of the extruder of the polymeric material, also in the case that such body has a relatively large mass.