If the object is to just take them out, any gun will do the job. If you are planning on using or selling the fur then use only head shots with a small caliber rifle and no shotguns. I agree that trapping is the most effective tool to remove problem beavers. (I will be heading out in just a few minutes to check my beaver line.) BTW, beaver meat makes excellent table fare. It is a very tender, sweet, red meat. We use it in place of beef. It makes great BBQ.