A machine (1) for wrapping bundles (2) of roll products (3), where the products (3) are grouped together in piles (4), comprises a bundle (2) forming line (6), equipped with a chain conveyor (7), and a product (3) feed line (12) that serves the forming line (6); the feed line (12) having an elevator (13) which is equipped with a product (3) supporting platform (14) and which is vertically mobile under the forming line (6) between a lowered position where it receives the products (3) and a raised position where it delivers the products (3) to the forming line (6); a screw mechanism, fixed to a fixed machine mounting structure and screwed on a lead nut placed inside a mounting frame, adjusts the position of the chain conveyor, the pair of pulleys and the pusher rods relative to the raised position of the product supporting platform.