Quiltsfor, I might be to casual about my mats but I just store them flat. One on the top of the other. Never had a problem with them. On the other hand I have a mid sized one that lives to the left of my machine for trimming and small cutting and a very large one that lives on the island in my kitchen most of the time. The others are small to mid sized and don't get much use. They are just stacked up waiting their turn.