Abstract: A polymeric heat shrinkable tubular sheath for mounting about a balloon on a dilatation catheter by heat treating at a temperature which does not detrimentally effect the properties of the balloon to shrink the sheath onto the balloon. The tubular sheath is preferably heated to a temperature above body temperature, e.g. 40.degree.<100.degree. C., preferably less than 85.degree. C., to heat shrink the sheath onto the balloon. A presently preferred polymeric material is a copolymer of ethylene(75%) and methyl acrylate (25%). The heat shrinkable sheath has an inner lumen with minimum dimensions large enough to facilitate the advancement of the sheath over the exterior of a dilatation balloon without the need for a great deal of manual manipulation by the physician or other operator prior to heat shrinking.