Winding glass ribbon by tensioning interleaving material

A method of winding a glass ribbon (10), including: winding an interleaving material (20) and the glass ribbon together to produce a roll (40); and tensioning the interleaving material so as to control a roll inter-layer pressure. By controlling the roll inter-layer pressure, the roll can be formed with straight side walls. The tension in the interleaving material can be controlled so as to be greater than 0 and ≦0.25 pounds per linear inch of width of interleaving material. Also, there is provided an apparatus for winding glass ribbon together with interleaving material into a roll. The apparatus includes: an interleaving material supply path; a glass ribbon supply path; a roll winding mechanism (46); and a means (26) for applying tension to interleaving material traveling along the interleaving material supply path, as the interleaving material is wound into roll (40), so as to produce a pressure between the layers of the roll.