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SHORT ANSWER: Wrap the base of trees with steel wire mesh that you can buy at any hardward store! Easy! You can just nail or staple it in place, or even just use the natural roll of the wire to wrap around the tree. Other plants are harder, and may require general fencing.
Before we start on the things you CAN try to get rid of beavers, we should first look at the methods you absolutely must not use to try and get rid of beavers. This includes poison, because it doesn't work and there isn’t a registered poison for an animal as large as a beaver that you buy commercially. This also includes trapping the creatures with the intentions of relocating and releasing them somewhere else. This is not usually not worth your time, money, or effort. To start with, the animal will more often than not die within a few days of you releasing the animal into the wild. The lucky ones that do survive almost never create a new den in the same area that they were released. If the beaver isn't released far enough away from the land on which it was trapped, it will just come right back. Removing one beaver alone won't solve your problem. Beavers form colonies that can run into double figures. Removing one just causes hard work for yourself.
Moving along from that idea somewhat, it is actually unlawful to release a beaver back into the wild once it has been captured in many states. The law dictates (in most places) that you can only release the animal on the land on which it was initially captured, which doesn’t get rid of your problem at all.
The best way to get rid of beavers is to look at methods that encourage them to politely wander off of their own accord. Destruction of the animal is one method of looking at things, but you will need to get in touch with your local city or county services to find out the trapping, release, and destruction regulations of a beaver. In many states across North America, the animal is actually considered to be a “furbearer”, and this comes with a number of regulations. Firstly, you'll need a permit in order to trap them or shoot them. Live traps CAN be used on personal property without a permit, but then you have the what-to-do-with-it-next situation. If you plan to use any other trap than a live cage trap to get rid of beavers, you will need to look at getting yourself a permit in most places.
You could always make sure that you are protecting the most-preferred plants and trees in your yard, but you must remember that beavers will often attack and chew at most tree and plant material, to use as material for construction if not for eating. There are certain trees and plants that beavers enjoy to eat the most, and these include:
Aspen tends to be the favorite, but no plant matter is safe. They will also eat other trees — trees that are not deciduous. Coniferous trees are the second choice, usually pine and fir trees, but as we’ve mentioned, they will use the wood they chew off as construction materials if they don't like the taste of it much.
The harder you make it for the beavers to reach the areas they want to get to, the higher chance you have of them giving up and looking for whatever they’re looking for elsewhere. Woven wire fences are a good idea to protect trees and smaller areas of plants and vegetation. Larger perimeter fences can be erected around your land as a whole too, keeping all manner of wild critters at bay, both large and small.
If you do have a problem with beavers on your land, don’t take matters into your own hands. Fences can help, as can those mesh wire fence protection systems too, but a problematic beaver with a dam will need to be removed and trapped by a professional. That’s a legal obligation, and not just a humane one.
Read more about How to keep beavers away from your trees or plants.
For more information, you may want to click on one of these guides that I wrote:
How To Guide: Who should I hire? - What questions to ask, to look for, who NOT to hire.
How To Guide: do it yourself! - Advice on saving money by doing wildlife removal yourself.
Guide: How much does wildlife removal cost? - Analysis of wildlife control prices.