In many cases of interest to experimentalists and geophysicists, the situation exists where a light, thin layer of material, such as glue or adhesive, is bonded to a heavier structure. If the layer is thin enough and if its acoustic impedance is small as compared to the underlying structure, then the layer can be thought of as having little effect upon the motion of the substructure. Thus, the effect of the substructure is to force motion of the thin layer. This paper considers the dynamic problem of a thin layer forced by displacements on the lower face and tractions upon the upper face. The exact solution is derived for the two‐dimensional case, while the three‐dimensional case is first considered using Bernoulli‐Euler‐Kirchhoff plate theory and, after this, including the effects of shear deformation and rotatory inertia. It is found that, if shear deformation and rotatory inertia are included, the theory is fairly accurate for problems in which the quarter‐wavelength of the disturbance is greater than or equal to the plate thickness.