A medical bandaging product (b 10) is rolled into a coil and positioned in a dispenser (11). Bandaging product (10) includes an outer elongate sleeve (13) formed of a moisture-impervious material and heat sealed along opposite, parallel extending sides to form an elongate tube. A medical material (14) is positioned within sleeve (13) and includes a substrate (16) formed of a suitable number of overlaid layers of a woven or knitted fabric such as fiberglass. Substrate (16) is contained within a tubular wrapping (18) formed of a soft, flexible non-woven fiber such as polypropylene. Substrate (16) is impregnated or coated with a reactive system which remains stable when maintained in substantially moisture-free conditions but which hardens upon exposure to sufficient moisture to form a rigid, self-supporting structure.