Are banana trees considered an invasive plant in certain areas. I have been growing them for several years in Virginia and they multiply quite dramaticly and survive our cold winters with no winter protection, I don't even cut them back anymore until the next spring. I have dug some up this spring to give to friends and noticed the root system has changed in the last couple years. It is much more dense, The next time I dig some up from the oldest area I will use a recipercationg saw instead of a shovel. Since we have a shorter growing season and they multiply and spread quickly, I expect in the warmer climate they may become a problem, but never heard of banana trees being a problem plant. I did a quick count and have over 70 trees in 3 areas. I am not complaining, I love the ease and how well they grow for me. Just wondering.