Closed‐form expressions have been derived for the driving‐point impedance, transfer impedance, and force transmissibility of circular and annular plates with clamped boundaries. The plates are internally damped and are driven either by a sinusoidally varying central point force or by one or more concentric ring forces of variable radii. The circular plates are mass loaded or elastically restrained at their midpoints, or are loaded by an ideally rigid annular mass (rib) of arbitrary radius. Computed results illustrating the frequency dependence of impedance and transmissibility are described, and their physical significance is discussed. Added mass is very effective in increasing plate impedance levels and in blocking force transmission to the plate boundaries, particularly when it is positioned directly beneath the driving force. [Supported jointly by the U. S. Naval Ordnance Systems Command, the U. S. Naval Ship Systems Command, and the U. S. Office of Naval Research.]