Dunnage making machine and method in which a web of paper is drawn across a forming bar with curved end sections to roll the edge portions of the paper, then drawn through a first throat section to urge the rolled edge portions toward each other and cause them to gather, and thereafter through a second throat section of lesser dimension than the first to gather the central portion of the paper and further gather the edge portions. The gathered paper is then pressed with a roller to crumple it, following which the crumpled paper is perforated along a serrated tear line.