Here are some great looking stuffed stork birds. Storks live in various parts of the world, while several species live in sub-saharan Africa and in Asia. Stork nests can reach up to six feet in diameter and ten feet in depth. Plush toy storks are not a common item to find. We have a couple of nice stuffed stork animals to choose from. Storks are commonly associated with a new baby, with the stork being the delivery carrier bringing the new baby in a blanket or diaper to the new parents.