Circular plate with a fluid on one side:The free and forced vibration problems of a clamped plate in an infinite baffle are solved exactly in terms of a set of self‐ and mutualradiation impedances Zmn(ω), associated with the normal modes of a plate vibrating in a vacuum. Computations of these impedances have been made for the lowest four modes over a sufficient range in frequency to solve theforced vibrationproblems that occur in practice as well as thefree vibrationproblem of these modes. The magnitude of the influence of the fluid on the plate is shown to depend only on the frequency of vibration and the non‐dimensional parameterβ = ρ0R/2ρh, whereRis the radius of the plate, 2hthe thickness, and ρ0/ρ the relative density of fluid to plate. Theshiftinresonant frequency, and thechange in shapeof the lowest four modes due to the reaction of the fluid on the plate are computed as a function of β. These changes are found to be important in the range 1<β<8. They are negligible for β<1, the case of radiation into air.