A higher-order boundary element procedure is presented for the free vibration analysis of flexible base plates of rigid fluid storage tanks resting on elastic foundation. The main principles of the procedure are replacing the biharmonic operator of the thin plate vibration problem by two successive harmonic operators, and representing the forcing terms (plate inertia, fluid loading and foundation influence) by applying the dual reciprocity boundary element formulation. The fluid effect on the plate dynamics is incorporated into the analysis by invoking another boundary element solution, which expresses the fluid pressure over the plate surface in terms of plate deflection. The performance of the method is thoroughly investigated and the nature of dynamic plate-foundation-fluid interaction is studied from several perspectives. The method provides excellent predictions, within the limits of Kirchhoff plate, potential flow, and Pasternak foundation models. (C) 2015 Elsevier Ltd. All rights reserved.