I own a sign shop and we have a material called PVC. It comes in different thickness but I use the 3mm and cut it to size and then round the corners. I had bought a Bag E Bottom when I made my first Margo purse. They are expensive !! This material works just great even without being covered with fabric. It won't bend like corrugated plastic or foam board.
Try your local sign shops or a plastic distributor. They will most likely have scraps since the material comes in 4' x 8' sheets.