Western hats keep their shape best when stored properly

Keep the front, back and underside of the hat from resting on a surface any way you can.

One way is to roll up a bath towel or sweatshirt in to a large, tight ball. Stuff this up into the hat leaving enough underneath that the hat sits up off the shelf. This keeps pressure off the brim of the hat and will keep the hat nicely shaped.

Or, if the hat has a firm crown, just turn it upside down and store it on its crown.

And never leave your hat on the dashboard of your truck. The heat and humidity will do irreparable damage.