A machine and a winding process receiving a continuous flow of flat and flexible elements (10) aligned along a longitudinal axis and partially overlapping, to form a spool (6) by rolling these elements into a spiral around a drum (8), with insertion between the turns of a flexible central strip (26), one end of which is fixed onto the drum and the other end of which unwinds from a hub (60) on which the strip has previously been wound, characterized in that the machine also includes a motor-driven resource (54) to regulate the transverse position of the hub (60) so as to perform lateral movement in relation to the spool (6) in order to maintain a constant alignment of the strip (26) during the winding process.