An apparatus comprising a dunnage conversion machine (30) for converting a stock material into a dunnage product, a stock material support (22) for a supply of stock material to be fed to the dunnage conversion machine, and a drop-and-slide mechanism (34) configured to allow the stock material support to be moved between an operating position and a loading position, which is spaced both horizontally and vertically from the operating position. The drop-and-slide mechanism includes a guide member (40) and a slide (42) to which the stock material support is mounted. The slide is supported by the guide member for horizontal movement relative to the guide member. A packer can pull the slide horizontally away from the operating position, causing the stock support to fall to the loading position, and the packer can push the slide away from the loading position, causing the stock support to rise to the operating position.