Abstract: This lay-up device for automatic positioning of a web of fibers on a mold comprises a lay-up head adapted to move under the control of a numerical control unit, in translation along three axes X, Y, Z and in rotation about the vertical axis Z as well as about a horizontal axis oriented in the direction of feed motion of the machine; the lay-up head (2) carries a roller (10) for applying the web of fibers (4) to be deposited on the surface (6) to be covered; the roller (10) is mounted on a support (18) connected to the head (2) by means of an articulation (20) about a horizontal axis of rotation X' which extends substantially in the direction of feed motion of the machine; this articulation, which is deformable without play (20) and has very slight flexibility, is constituted by a full portion reserved between two slits (22-22') formed between the main support (16) and the auxiliary support (18) of the head (2).