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ABSTRACTThe purpose of this paper is to derive an effective method of analysis of dynamic behavior of plate-like structures interacting with an ideal fluid. We introduce the basic relations describing small harmonic vibrations of elastic plates lying on an ideal fluid and study some essential properties of the corresponding mixed boundary-value problem. A potential noncompressible fluid theory has been used to estimate hydrodynamic forces acting from the fluid outside the plate. An analytical solution of the exterior hydrodynamic problem with two-dimensional plane motions of the plate and of the fluid is derived. The derived analytical expression for hydrodynamic reaction has been taken into the structure equation to derive a closed one-dimensional differential–integral equation of floating structure vibrations. The formulation and the study of the variational problem of vibration analysis for plates interacting with a fluid are performed. The proposed partly analytical approach radically simplifies the analysis problem and minimizes the volume of computations.* Communicated by I. Elishakoff.