Summary: The authors present a modern theory of thin elastic plates with transverse shear deformation where the disturbance is represented by a train of harmonic waves. Dirichlet- and Neumann-type problems are formulated together with appropriate radiation conditions (in the case of the exterior domain). The paper shows that uniqueness for exterior problems is guaranteed for a range of flexural waves. In the interior problems, the presence of eigenfrequencies means that there is no general uniqueness result. The paper also indicates how corresponding results can be proved for micropolar plates.