this invention relates to packaging &# 34 ; sleeves &# 34 ;, or multi - sided , tubular structures which may be used for packaging articles , as blanks for boxes , or the like , which are made from multiple layers of spirally wrapped strips of paper , fabric , or the like ; which sleeves may have discrete corners at the junctures of their sidewalls , which corners may be permanent where rididity is desired , or foldable so that the sleeves may be flattened for storage and / or shipment . such sleeves may be made by apparatus , and / or utilizing methods , in accordance with the present invention , which contemplates the formation of a substantially cylindrical core over a cylindrical spindle , and transferring the core to axially oriented lines of rollers which are oriented radially to the axis of the spindle at sequentially increasing distances therefrom , whereby the sleeve , while still softened from the application of glue to its constituent layers , may be permanently distorted into its desired multi - side , multi - cornered configuration , with desired radii at the corners and such grooves as may be desired to augment hinging to facilitate flattening of the sleeves .