As with virtually all phenomena studied in modern acoustics, fluid loading of a vibrating structure caught the attention of Lord Rayleigh. In his “Theory of Sound” [l, Art 3021, he analyzed the “reaction of the air on a vibrating circular plate”, showing that reaction to be equivalent to a virtual mass and radiation damping, to be added to the plate mass and the mechanical damping. His calculation was for the case of specified uniform motion of a plane, circular piston embedded in a rigid baffle, which permits immediate evaluation of the radiation field by quadrature over the values of normal velocity, known over an infinite plane. Nonetheless, his description of the fluid loading in local added mass and radiation damping terms is general, and complete. However, it does not exhaust interest in fluid loading problems because the integrated result, over a large vibrating structure, of such local effects (usually phased by some travelling wave mechanism) can have a quite diflerent qualitative form, and also because the added mass and radiation damping depend on the vibration mode shape and mustin a fully coupled problem with significant fluid loading-be determined simultaneously with the structural vibration and fluid motion. Techniques for dealing with such fully coupled motions of elastic plates and shells immersed in air or water were simply not available in Rayleigh’s time, but have become available in the past three decades or so. On the analytical side, much progress has been made using complex integral transform techniques and methods of asymptotic singular perturbation theory, while finite-element and boundary-integral-equation methods have clearly emerged as leading computational techniques in this field. A standard reference (though not including the most recent results) on the analytical modelling is the book of Junger and Feit [2], while developments in computational acoustics have been described in reference [3]; mention should also be made here of the “doubly asymptotic approximations” (DAA, , DAA2) which form a hybrid analytical-computational scheme (see, e.g., the paper by Geers and Felippa [4]). These advances in scientific understanding have been driven by widespread occurrence of technological processes in which fluid loading of vibrating structures is important; examples abound in marine engineering (vibration and acoustic fields of ships and submarines, vibration of oil rigs and submerged pipelines), in aeronautical engineering (aircraft and helicopter structures vibrating in air, and the internal loading of aircraft fuel tanks), and in mechanical and nuclear engineering (vibrations of ventilating systems