Expressions are stated for the transmissibility and for the driving‐point impedance of an internally damped circular plate of radiusawith a clamped boundary that is driven by a vibratory point force at an arbitrary distance μafrom the plate center. Expressions are also stated for the plate transmissibility and driving‐point impedance when the plate is loaded at the arbitrary driving point either by a lumped mass, by a dynamic vibration absorber, or simultaneously by a lumped mass and a dynamic absorber. In all cases, representative calculations of transmissibility and impedance are plotted versus the square root of frequency. These curves clearly show the dependence of transmissibility and impedance on the plate damping factor, the value of the parameter μ, and the extent of the mass loading. They also show the effectiveness of the dynamic absorber, which varies with the value assigned to μ.