An unpowered, manually operable apparatus for dispensing cushioning wrap material drawn concurrently from a roll of separator material and a self-contained cartridge that includes a roll of expandable sheet material. The rolls are supported on a stand for rotation about respective parallel, spaced-apart axes. In addition to the roll, the cartridge includes a tensioning assembly and support panels that abut respective ends of the roll. The tensioning assembly and the support panels cooperate with the stand to control rotational resistance of the roll. The rotational resistance causes the expandable sheet material to expand in length and thickness as it is manually pulled from the stand with the separator material, and support surfaces on the stand hold the cartridge and the separator roll in position. When the cartridge containing the expandable sheet material is depleted, the cartridge is readily removed and replaced.