A system (10) for automatically dispensing a strip of dunnage to a container (14) includes a dispenser (12) having an outlet (92) from which the dispenser can feed a length of a strip of dunnage lengthwise, a container support (36) for supporting a container (14) thereon, and a pusher device (114) at the outlet (92) for pushing, more particularly propelling, a trailing end of the strip of dunnage from the outlet (92) toward the container support (36). The outlet (92) is aligned with the container support (36). Thus the outlet (92) is positioned relative to a container (14) such that the strip will curl or fold back and forth upon itself within the confines of the container (14) as it is being fed from the outlet (92). A container closer (120, 130 and 32) automatically closes the flaps (80 and 82) of the container (14).