Sound radiation from thin metal plates has consistently been recognized as a severe noise problem. One of the most popular approaches to suppressing this noise is applying viscoelastic layers, also called free layer damping (FLD), on the plate surface, which can damp the structural motion and minimize the radiated sound. The thickness of the FLD is an important parameter. It needs to be optimized for the target acoustic limits through numerical simulations, as the total mass and the costs may rise unnecessarily. This paper investigates the sound radiation from thin metals of particular sizes with different thickness values of FLD. A unique test setup was established to measure vibration and sound for three different sized plates, with each one having three different FLD thicknesses, namely, 0.5 mm, 0.75 mm, and 1 mm. In parallel, vibro-acoustic analyses were performed for the same configurations using the finite element method. The damping of the FLD was defined using the Rayleigh damping model, of which coefficients were obtained through a prediction formula developed earlier by the authors. After validating the model with the test, the effect of FLD on the extended acoustic parameters (radiated sound power, directivity) was also analyzed.