I buy 4" diameter tubes from the local company that mostly supplies bubble wrap and other shipping supplies. They happily cut them to length and supply plastic caps. About 1/4" thick walls protect from just about anything, as Brian pointed out go for thickness. You can apply a large piece of tissue or other roll paper to your print before rolling it up. Always best to roll up on a smaller diameter tube, the will expand once inserted inside your shipping tube. Avoid diameters below 3" as they will put a curl on you art that is hard to remove. If you use really large diameter tubes your print might collapse inward, so stuff the air space with crunched up paper.
Would really not want to use anything flat. But if absolutely necessary get Lowes etc to cut up a piece of dirt-cheap 1/8" Masonite just a little bigger than your print, wrap your print in paper, then tape that to the Masonite. Top the exposed side with some cardboard.