The car body panel gets thinner as automotive lightweight technology advances, which affects NVH performance. To achieve the desired noise control, both radiation and propagation paths should be taken into consideration. It is suggested that Passive Constrained Layer Damping (PCLD) can be used to address the problems. In order to efficiently assess the acoustic vibration properties of a sandwich plate with a viscoelastic core, the coupled finite element and boundary element (FE-BE) method is used. The four-node plate element is used to simulate the plate. The direct boundary method is used to solve the Helmholtz wave equation for air. The coupled FE-BE method is used to calculate the radiated sound field under point excitation. The sandwich plate is made of two aluminum plates bonded by structural adhesive. The dynamic mechanical parameters of the adhesive are obtained by the modified Oberst method, which uses a composite beam with an aluminum base beam and a layer of adhesive. Then, the master curve is applied in the coupled FE-BE procedure. The acoustic pressure is measured by a microphone when an impact hammer hits a sandwich plate. Comparisons with both impact tests and the proposed FE-BE method are shown to prove the accuracy and computational efficiency for the modeling of the vibro-acoustic response of the viscoelastic sandwich plates.