The most sure way I have seen of shipping an unframed but matted print is to wrap the matted print in plastic, sandwich that between two pieces of scrap mat and then sandwich that between a couple peices of either 1/16th or 1/8th masonite. Tape the edges with strapping tape and then wrap with craft paper for labeling. Can get heavy for something as big as 30x40, but nothing will bend the matted print and nothing (well almost nothing) will puncture the masonite. The same for a framed print, just put the scrap mat board between the masonite and the frame to prevent any marring or scarring of the frame surface. With a frame you would need to put the whole thing in a box or build a box out of cardboard. If the print is really valuable or irreplaceable I would build a wood box for shipping.
Maybe Dave Parker can chime in about how he packages his ground glass. I got several as big as 12x20 in fine shape. If thin glass can make it unbroken, his packaging is probably more then adequate for a matted print.