It is known that hard planar acoustic screens generate null far-field amplitude on the directions defined by the plane that encloses them. We proved in an earlier paper that this property actually characterizes plane screens among scatterers of any shape, and we generalized it to other boundary conditions. Furthermore it wits proved that a single incident wave is sufficient to distinguish screens that lie in the same plane. Generalizations of these results are carried out in this paper to the elastic case.