Easiest way to store your Silpat is to lay it inside your clean cookie sheet and nest another cookie sheet on top. That way they are always stored flat and protected by the cookie sheets. I've had the same three Silpat sheets for 10 years and have always stored them that way.
Agree with EA...definitely store them on your sheet pans...just make sure all is dry before nesting them with each with its individual Silpat in place. I have 4 pans and 4 Silpats...the only way to fly!
I found a product on Amazon called the Silicone Mat Rack Fox Run Brands Silicone Mat Rack (click on the product link to see a nice video review done by another reviewer). It lets me store my Silpats vertically in my tall cupboard next to my baking sheets, very convenient (I can store more than one in the Mat Rack). It also lets you put your Silpat in the dishwasher like a cutting board. I know the instructions say only hand wash but like others I have jerry rigged mine in the dishwasher for years after using with oily or savory dishes, never a problem. But you can just use it for storage if you aren't comfortable with that.
I have just gotten mine, which I intend to store between my two half-sheet pans. However, they arrived each folded in half, in a plastic envelope. I will certainly watch to see if they are weakened along the fold line.