I actually have an art tube that will do the job...its storing mine!
Its a hard plastic tube, about 3' in length or so, with a screw top lid. Screw-on extensions are available, letting me store & transport my mat, along with a baggie of markers for it.
But its currently on loan (with the mat inside) at our game group's host's house, so I can't go look at it and tell you its name. However, I do have another tube by the same company storing yet another mat.
As soon as I find it- or after game night (this coming Tuesday)- I'll let you know the brand name.
I also know that there is at least one other company that has a telescoping art tube that would do the job. I had ordered one from an art supply place and put my money down and was waiting for it to come it. For months.
I went in to check on it's arrival time, and they stated they didn't do special orders. After showing them my receipt, I got my money back, at least.
Needless to say, I don't do business with those morons anymore.