This is how I store my terrain mat, rolled up in a cardboard tube.
A large mat wraps around the tube, my desert map fits inside.
It needs a couple of minutes for the edges to relax and lie flat after you unroll it!
Desert buildings have had their bases repainted and palm trees have been finished.
The mat is very resilient and extremely flexible.
Because it's so thin, the frame sealant layer doesn't crack or flake and the stretchy leatherette allows you to position small objects under the mat to vary the shape of the terrain.