An apparatus for clamping packaging material may include a packaging material holder. The packaging material holder may include a first jaw, a second jaw, opposing the first jaw, and a jaw opening between the first and second jaws. The jaw opening may be configured to receive a portion of packaging material. The packaging material holder may include an inflatable structure configured to fill at least a portion of the opening. The apparatus also may include a packaging material insertion tool configured to insert the portion of packaging material into the jaw opening for clamping.