Yes, the elf on the shelf can move. It is a magical elf who is enchanted to have a life of its own, which means it can move around and interact with the environment. The elf is usually placed in a prominent location in the home, such as on a shelf or in a window, and is able to move to different spots each day. The elf's job is to observe and report back to Santa Claus, so it needs to be able to move freely in order to keep track of the children's behavior.