I have been storing in cedar chest for years till I ran out of space, no its plastic boxes with silica packets inside, never had mold, and I am in South Fla, HUMID! You could try wrapping individual pieces in white tissue such as comes with clothing, and storing on shelves. In order to identify, photocopy piece of fabric, on back side write the amount of fabric in cut, this way you don't have to unwrap to see or measure