Abstract: Improved pneumatic shafts, chucks and lifts for roll stock and methods of construction and operation comprising an air bladder housed within a pair of concentrically disposed, longitudinally slotted sleeves. Upon inflation of the bladder, the outer sleeve expands against the roll stock, or the core supporting the roll stock, providing full length grip. The inner sleeve expands against the outer sleeve while protecting the bladder from being pinched. The bladder is preferably a vinyl polymer plastic containing substantially inelastic roving to provide controlled and limited expansion. The combination permits true centering of rolls for rotational balance and constant tension, true running.