The boundary element method of analysis is applied to the calculation of hydrodynamic pressures in a reservoir impounded by a gravity dam and subjected to a harmonic ground motion., It is shown that the differential equation governing the small amplitude vibrations of the reservoir reduces to the familiar Helmholtz equation. This equation is converted to an integral equation which involves integrations only on the boundary of the reservoir. The integrals are evaluated numerically by using a series of straight line elements to represent the boundary. The resulting simultaneous equations are solved by standard techniques to obtain the pressures and pressure derivations on the boundary. Analytical results are presented to show that the proposed method gives results that are in good agreement with the known classical solutions. The method is then applied to the solution of vibration problems of reservoirs with irregular boundaries for which classical solutions do not exist. The method is also successful in dealing with cases of infinite reservoirs and in modelling the energy loss in the waves moving to the infinity.