I just finished building a work table in my studio and one of the things I had to include was storage for 32x40 sheets of mat board. My solution is pretty simple–it may work for others. Since I have found that flatfile storage takes up too much floor space and standing the boards on end often leads to them bowing if the box is not full, I took a piece of 1/2" MDF 36x48, added a small ledge along one long edge and mounted it at about a 30 degree angle off the back of the table. The boards sit flat against the MDF and the total floor space required is much less than a flat file needs. A drop-cloth attached to the top edge of the board keeps them covered and relatively dust-free. Since the entire table is on wheels, I can roll that side up against the wall and the boards are really out of the way most of the time. If the acidity of the MDF is a problem, a barrier sheet between it and the mat board is always easy to add.
I tend toward rather rough and ready solutions, so my version isn't pretty, but it works. The design could be made far more attractive with higher quality material and better craftsmanship, but the key is to have it all on a slant so that the boards are kept flat by gravity without taking up a lot of floor space.