I have a collection of veneer pieces that I need to store (possibly for months or even years). Their size varies from less than a foot in length to around 8 feet long. Sandwiching veneer between two sheets of plywood or MDF [and optionally wrapping them in shrinkwrap] has been recommended. I can do that with the smaller pieces, but not the longer ones. Is it OK to roll them up for storage? I understand longer veneers are shipped that way.
The consensus is to store veneers flat. If you don't currently have somewhere suitable for the longest pieces consider installing a shelf high on a wall somewhere (or even from the ceiling!) in the home or garage so that it can be.
Some quotes (my emphasis):
Most veneers come as flat sheets, although flexible (paper- or adhesive-backed) veneer may be sold in a roll. Always unroll these materials and store them flat.
Rolled veneers should be carefully unrolled as soon as possible and kept flat in a horizontal position.
Long wood veneers are typically rolled up for shipment. Once they arrive, it's best to slowly and carefully unroll the veneer and then store it flat.
Most sources also agree about wrapping in plastic being advisable to prevent veneers from drying out (note: even in the UK, where humidity is consistently higher than in most of the US; so neglect this at your risk).
The most-mentioned material for this is shrink-wrap as you mention in the Question, and occasionally black shrink-wrap. Trash bags are also frequently suggested, and sometimes also plastic sheeting sold in roll form. Obviously shrink-wrap will do the best job here. The last will be least effective at keeping the moisture level constant unless you tape all the edges with something like duct tape, but just as a laid-on cover a plastic sheet is still better than nothing.
More info and further tips in the following links:
The Proper Storage of Raw and Backed Wood Veneer on the Herzog Veneers site.
Storage strategies for paper-thin veneers from Wood Magazine.
Storing (and Flattening) Veneer on WoodWeb.
Store Veneer Flat on Fine Woodworking (note: behind paywall).
Some random other quotes I came across along the way that I thought could be of interest:
Typically, there is no "shelf life" to a veneer when it is stored properly. I have used elm burl veneer that was sliced in the early 1970's and there was no problem.
Some of my best veneers are stored under my bed!
If long-term storage is anticipated, [Jonathan Benson] recommends taping the ends across the width with veneer tape or high-quality masking tape the day the veneer arrives, before it can dry out at all, to prevent splits.