This press for forming cylindrical or round bales comprises sets of bands or belts which, in a conventional manner, define a chamber for forming a bale by rolling up, as well as a pickup designed to transfer harvest products gathered on the ground as far as a bale-forming chamber through an entry opening for the products, and a starting roller located on that side of the opening that is remote from the pickup. According to the invention, a scraper is arranged to cooperate with the starting roller in such a manner as to resist any rolling up of the harvest products around the roller. If the roller is a smooth circular section roller, the scraper may be stationary. It may be arranged in conjunction with fingers extending between the bands or belts as far as to the immediate vicinity of the starting roller on the side of the roller remote from the scraper. In the case of a noncircular starting roller, the scraper is mounted so as to be movable, especially pivotable. It may be resiliently urged towards the starting roller, or else be positively displaced by a driving mechanism.