A plies sleeve for use in forming a core of plies and beads on a core build mandrel where the plies sleeve is woven as a tubular sleeve having a uniform circumference that will stretch laterally, increasing the sleeve circumference to fit over a top surface or crown of the core build mandrel and is of a length to where each sleeve side will fold down an opposite core build mandrel side, passing around a tire bead, back up the cored build mandrel side and over the top surface or crown edge. Which outward sleeve stretching is provided by a select weave where Rayon cords are spiral wound as vertical components of approximately seven point (7.5) pics per inch, and elastic cords are included as horizontal components of approximately eight (8) pics per inch that are formed as pre-cure elastic cords from a urethane material and are cotton wound, to allow for sleeve stretching and provide for a return of the plies sleeve to its un-stretched state.