Abstract: A machine for automatically draping and compacting including a draping head that grasps, deposits and compacts fiber plies on a draping support, the draping head including first and second rigid supports and a gripper including a piece of elastically deformable material having a face to grasp a ply and intended to bear against a draping support surface. The first and second supports are connected to, respectively, a robotic handling device and to the first support and to the gripper. The draping head includes bearing force or pressure measuring elements between the first and second supports or housed in the first support. A control unit is connected to the bearing force or pressure measuring elements to monitor a compaction bearing force or pressure applied by the draping head.