A system and methods for wrapping bales in a harvester uses wrapping material stored in flat, folded layers instead of conventional round tubes or rolls. The system includes a material support tray at least one feed roll, and at least a first tensioning element. The material support tray is capable of supporting at least one bundle of wrapping material. The first tensioning element is positioned adjacent to or in the material support tray and is in operable contact with at least one bundle of wrapping material.