A machine for cutting and stacking into layers sheets of a pre-established size from a plurality of strips of wood obtained from a piece of veneer. The pieces of veneer are fed into a cutter by means of a first conveyor belt actuated by a control means which detects flaws in the wood to cut out transverse strips containing the flaws that are then automatically discarded as they come off the cutter. Strips free from defects are then sent on by a second conveyor belt to a deflector which distributes the strips onto two conveyor belts with intermittent movement so as to arrange the strips into compact adjacent groups to form a sheet of desired length. The plurality of adjacent strips forming a sheet are then sent to stackers to form layers of the sheets.