An apparatus for winding a flexible thin-walled tubular material, radially of itself into a plurality of overlapping reverse pleats for storage and subsequent unwinding or feeding comprises: a hollow guide member and means for supporting the guide member for rotary movement, a support member, and means for supporting the member for rotary movement, a supporting means permitting longitudinal movement of at least one of the members relative to the other, means for rotating the guide member and support member in opposite directions, and means for moving either the support member or guide member or both longitudinally and reciprocally whereby the support member is reciprocated into and out of the guide member. When flexible tubular material is passed over the guide member and secured to the support member, the rotary and reciprocal movements of the members are effective to cause the tubular material fed thereover to be wound in a plurality of overlapping reverse pleats.