This support system serves as an alternative to solid polyethylene cores when constructing for basketry hats that cannot rest safely on either the brim or crown. The rolled polyethylene sheeting provides as much support as a solid polyethylene foam plank and more than quilt batting or polystyrene beads. The sheeting takes less time to shape than solid polyethylene foam planks and is easier to handle than the beads. The hat supports can be made from scrap pieces of polyethylene foam sheeting left over after cutting sheets to line drawers and shelves.