An apparatus (100) for making glass tubing (200) of a desired non-circular cross-sectional profile (cf FIG. 3) includes a mandrel (101) adapted for positioning proximate heat-softened tubing. The mandrel (101) has a nose (102) and a nozzle section (120) with a chosen profile that will define a final cross-sectional profile of the tubing. The nozzle section (120) has a feed chamber (140) for receiving a gas from a source (207) and a porous and/or foraminous circumferential surface (132,134) through which the gas can be discharged to an exterior of the mandrel. The gas discharges to the exterior of the mandrel, forming a film of pressurized gas in the gap (314, 318) between the porous circumferential surface (132,134) and the heat-softened tubing (200). A method of forming tubing having a non-circular cross-sectional profile using the apparatus is also provided. A glass sleeve made from the reshaped or formed tubing is also disclosed: a monolithic sleeve made of parallel, opposite, flat and smooth front and back covers for use in an electronic device (cf FIG. 13). Some glass-ceramic materials may also be suitable for the tubing, such as transparent beta spodumene.