A dunnage crumpling apparatus is provided having first and second entry-side crumpling members and first and second exit-side crumpling members. The first and second entry-side crumpling members define an entry therebetween. The first and second exit-side crumpling members define an exit therebetween that is disposed along the longitudinal path downstream of the entry. A crumpling zone being defined between the entry and exit. The first entry-side crumpling member is configured for moving at an first rate and is associated with the second entry-side crumpling member for moving sheet material through the entry in a first direction along a longitudinal path at an entry rate. The first exit-side crumpling member is configured for moving at an second rate and is associated with the second exit-side crumpling member for moving the sheet material through the exit in the first direction along the path at a exit rate that is slower than the entry rate to crumple the sheet material for producing dunnage. The entry and exit-side crumpling members are displaced laterally along the path with respect to each other to cause shearing of the sheet within the crumpling zone.