This paper presents a finite element model for sound transmission analysis through a double sandwich panels with viscoelastic core inserted in an infinite baffle. The proposed model is derived from a multi-field variational principle involving structural displacement of the panels and acoustic pressure inside the fluid cavity. To solve the vibro-acoustic problem, the plate displacements are expanded as a modal summation of the plate’s real eigenfunctions in vacuo. Similarly, the cavity pressure is expanded as a summation over the modes of the cavity with rigid boundaries. Then, an appropriate reduced-order model with mode acceleration method by adding quasi-static corrections is introduced. The structure is excited by a plane wave. The radiated sound power is calculated by means of a discrete solution of the Rayleigh Integral. Fluid loading is neglected. Various results are presented in order to validate and illustrate the efficiency of the proposed reduced finite element formulation.