In this paper, we present a finite element formulation for vibration reduction in structural-acoustic systems using passive or semipassive shunt techniques. The coupled system consists of an elastic structure (with surface-mounted piezoelectric patches) filled with an inviscid linear acoustic fluid. An appropriate finite element formulation is derived. Numerical results for an elastic plate coupled to a parallelipedic air-filled interior acoustic cavity are presented, showing the performances of both the inductive shunt and the synchronized switch shunt techniques.