Abstract: An insulating holder for a hot or cold drink cup including a tubular sleeve member that is made of a cellulosic paper material and has top and bottom circular openings that enable the sleeve member to be fitted over the liquid container. The tubular sleeve member has its top and bottom openings sized so as to form a frusto-conic shape when fitted on the cup. The tubular sleeve member is provided with a plurality of folds that each extend in a direction between the top and bottom circular openings and that each extend substantially in parallel with an adjacently spaced fold. Each fold defines an air channel that is formed on an inner surface of the tubular sleeve member and that extends along each fold for providing insulation by virtue of the air passage between the holder and cup. The folds extend in a direction that includes a transverse component so as to inhibit compression by the user at the fold. The holder also includes microscopic air chambers which are used to absorb and retain moisture.