Tyvek crate lining

What is the best way to line the inside of a crate with Tyvek? And how do you adhere ethafoam to the Tyvek?

FIRST adhere your foam where you want it. THEN cut Tyvek larger than what you need and lay it in the crate, sticking it down with hot glue in small amounts.

So there isn't any barrier where the ethafoam blocks are?

Your post confuses me a bit in that I have not seen a CASE lined with Tyvek as far as I can recall. Generally, the case is built, lined with a buffer of some sort that SNUGLY fits the art work therein and then the artwork is wrapped in Tyvek - sealing the seams with packing tape. Sometimes the art has its own box within the crate...sometimes the foam/buffer is custom cut to match the contours of the shipment item.

Lining Crates with smooth or "hard structure" Tyvek was a common thing for a long time and is still specified by some museums. It looks really pretty but in terms of function it is a little "Iffy". For one thing while Tyvek is a "waterproof" material (you can make a bag that will hold water with it) and therefor it will may prevent water damage if the joints of the crate are compromised (if it takes a huge hit) it is not an effective vapor barrier which means won't prevent harmful by-products offgassing from wood products (acids or glue pollutants) from concentrating within the enclosed environment of the crate where your art is living. For that reason it is not normally specified by most museums these days.
If you are using it to line a crate for whatever reasons, there are a couple ways to approach it. One is to line the crate and then pre-locate where your foam will go and then cut out those areas so that the foam can be glued directly to the plywood underneath (the obvious problem here is that by doing so you have compromised any real value it has as a barrier to either off gassing or moisture). Another method is to adhere the Tyvek with a layer of wood glue (usually rolled on like paint) between the ply and the Tyvek. This results in a more stable surface to glue foam blocks to that will actually allow the Tyvek to function as entended. The biggest concern about the use of Tyvek lining actually comes into play where the crate joints occur and those issues envolve potential structural compromise of the crate structure and are worthy of another post all together. If you are committed to using Tyvek as a liner let me know and I can post a couple of illustrations that should be helpful.

Thanks for all the info. Sounds like the best and most practical solution is to wrap the object instead of trying to make a more esthetically pleasing crate with a Tyvek liner

Wrapping and sealing individual pieces is usually considered desirable regardless of the construction of the crate because it creates a sub-environment within the enclosure (an exception would be if the objects have been maintained in a high humidity environment in which case there could be condensation issues). Alternates to Tyvek are Marvelseal which is a true barrier material isolating the crate contents from humidity problems and off gassing and Somewhere in between marvelseal and plywood is MDO which is an exterior grade plywood made with a plastic coated paper finish that is preferred by some.

YES! Wrapping.

Using Tyvek in crates is not very effective as it has been mentioned above. It does offer a clean interior compared to exposed plywood walls. Wrappping the internal packages is a more straight forward approach to protecting the contents. Some poeple have used primed MDO plywood and sealed the seams to give an overall barrier but not sure how well that performs.