I too assume you mean MODEL aircraft - like the last poster, I can't see that such a full-size aeroplane would be strong enough or light enough to fly successfully - or at the very best, not with enough payload of any sort to make it a practical proposition.
But if you mean model aircraft, then Yes, there are many examples: 1. Before about the early 1950's (I think) and the advent of plastic kits, aircraft models were made from solid wood, both from balsa, and "ordinary" solid wood. They were primarily for display only, and especially during WWII, for learning to recognise different aircraft types. I myself made one or two (from balsa) but it was MANY years ago. 2. They're still made today, from both solid wood (and from cast plastic and metal), mainly for display purposes, e.g. travel agents windows, aircraft manufacturers, desk top displays, collectors, etc. There are companies who specialise in such work (ship models too). And 3. As already shown above, like the nice model helo and floatplane, mainly from solid wood, as children's toys. 4. Nearest to actually "flying", the specialist models made for aerodynamics research in wind tunnels (though a lot of that is done with computer "virtual" models rather "real" models these days.
But in none of the above cases are they intended to be models that will fly (much too heavy, and usually, the balance point ("CofG") completely in the wrong place) - unless I s'pose someone threw one out of the window in a paddy.