When the thickness of the elastic body is small, lower dimensional theories have been proposed, depending on mechanical and geometrical nature of the body, as approximations of usual three-dimensional theory. But it is not evident which is the model most suited to a particular case in mind. Consequently, before approximating the exact solution of a given lower dimensional model, we should first know whether it is “close enough” to the exact solution of the three-dimensional model it is intended to approximate. Thus one is lead to the question of mathematically justifying lower-dimensional models starting from the three-dimensional model.