A self-wrapping dilatation balloon comprising a multiblock copolymer having high elasticity and elastic recovery from nominal strains greater than about 30% is described. Also described herein, is a polymeric extrudate for making a dilatation balloon comprising a multiblock copolymer having tensile strength in the range of about 50 MPa to about 450 MPa, strain at break in the range of about 50% to about 600% and substantially complete elastic recovery from nominal strains of at least about 30%. The extrudate has phase-separated microdomains that are macroscopically aligned in parallel, perpendicular, transverse or a combination thereof. Also described herein is a process for producing a polymeric extrudate for use as a dilatation balloon. The process comprises extruding a multiblock copolymer mixture or composition to form an extrudate. The extruding is done such that the extrudate has phase-separated microdomains that are macroscopically aligned in parallel, perpendicular, transverse or a combination thereof. After extrusion, the process optionally comprises the steps of drawing and coagulating the extrudate.