It depends on what you want to achieve. Wire mesh would work to keep out burrowing animals if you attached it to the bottom of your frame. Plastic on the sides would prevent contact between the wood and the soil, but plastic is no good for the bottom because it impedes drainage.

Thanks for your reply! I want to preserve the wood. I was worrying that the plastic on the walls may block airation in the soil and that the wire mesh would allow the soil to breathe somewhat better. If the plastic on the walls is not an issue with air and soil moisture, I will put the plastic on the walls and also use wire on the bottom. Although I'm double digging under the bed anyway and building 2 foot deep walls for the beds.. Then mixing the removed foot of soil with equal parts of Spargum peat, course sand and 3 year old composted cow manure.we have clay soil here.  Any thoughts on that soil mix?

In our area in Carbon County, purchased compost means mushroom soil and purchased top soil is heavy in clay. I've ended up adding perlite (a calcium product) to lighten it up. It's easy when you are adding mushroom compost, composted manure and sphagnum to get an acidic pH. Also, I made the mistake of ordering the top soil and the mushroom soil separately. If your landscape supply has something they call raised bed mix or potting soil mix, you'll save yourself the horrible job of trying to mix it yourself without a front end loader.
Here is a link to an organic gardening website I found very helpful in thinking about the soil mix and my raised beds. It's a reality show on PBS where the host went through an entire year making raised beds and taping the good the bad and the disasters.
One thing I didn't expect was that the horizontal boards on the long sides began to bow out from the pressure of the wet soil. I found it helpful to drive stakes to help support the sides. In fact, we used a thing called masons pins, long metal pipes with holes that can accept screws.
I wish you good luck. Getting the project together was a race against time for me last year, but everything I planted grew twice as well as it did on flat ground.

Thanks very much Eileen. Big help to me!!!

Thanks very much Eileen. Big help to me!!! I'm not using mushroom soil. Steve Bogash, Penn State Tomato guru, advised against it. Much of it use to have a nasty hay herbicide in it very toxic to plants. I'm using 3-4 year old composted cow manure. I'll check out perlite, I was under the impression that it very crazy expensive. I'll look into it!

The place to buy perlite is a masonry supply. They use it to lighten up mortar and concrete mix. It's very expensive through a garden center, but not at a masonry place.
Thank you for that tip on mushroom soil. I think I got a batch with a pesticide residue in it. I had a lot of seedling death on one bed. I wondered if it was something like that.

Steve Bogash use to do all the Tomato trials for Penn State. I met him in a couple of classes. He's a great guy and very knowledgeable. He told me to steer clear of mushroom soul because many growers lost complete rows of crops from a herbicide use to kill everything but hay being grow specifically for the mushroom growers in their soil mix. That was a few years ago, like 3-5 years. I will not use mushroom soil as two of my friends got a bad batch and lost a lot of plants.

Thanks again. For me it's a lesson learned.

BTW how much perlite would I use per cubic yard? 25% top soil, 25% well composted cow manure, 25% course sand and 25% Sphagum peat moss? Any idea?

When I filled my raised beds I used the 60% top soil 30% compost 10% perlite rule.
I used a 5 gallon paint bucket from the home improvement store and threw in 6 buckets of topsoil, 3 buckets of compost, and 1 bucket of perlite. Then I mixed and looked at the soil. That's when you make adjustments using the squeeze test. You squeeze a handful of the mix. It should hold together but crumble if disturbed. I watered it down and then it rained. I lost about four inches. When it dried I tested it with the squeeze test. The damp was about the same as a rung out sponge, and there was no pooling. Your sand might count for perlite since it does the same job. Your top soil is a lower ratio than my formula. I would mix it as is before you add anything else. If it seems heavy, then the perlite could help. You might not need it.