An approximation method is presented for solving the equations of motion that describe the vibration of an elastic structure immersed in an infinite acoustic fluid medium. The mathematical model that is developed uses the finite element method to calculate the vibrational characteristics of the elastic body and the acoustic pressure field of that portion of the fluid which closely surrounds the vibrating body. Analytical methods are used to obtain the boundary conditions for this mathematical model. This technique can be used to predict the response of an elastic structure over a wide range of frequencies and the acoustic pressure at a large number of field points in both the nearfield and farfields. It avoids the difficulties encountered at eigenvalues of the interior problem by determining exactly the one degree of freedom needed to overdetermine the surface equations. Experimental validation of theoretical predictions is given for a piezoelectric cylinder, and a computer‐generated contour plot of a predicted nearfield pressure distribution is shown.