A device for applying pieces to absorbent articles includes a supporting shaft rotating an axis; anvils rotating about the axis; a cutting unit operating with an anvil contact surface defining a cutting station for cutting a web into pieces; pads, each having a retaining surface for a piece, are moved about the axis for conveying a piece from the cutting station to a releasing station for release onto a substrate. Each pad rotates for varying the orientation from the cutting station, where the larger side of the pad is parallel to a feed of the web, to the releasing station, where the larger side of the pad is transversal to the feed of the receiving substrate, and vice versa. Each pad translates parallel to the pad axis, away from and towards the shaft axis. Each pad has an oscillating movement about its own axis.