In this study, transverse vibrations and acoustic radiation of an all-edges-free baffled rectangular thin plate are examined by Rayleigh's formulation. While the Rayleigh-Ritz method is applicable for a wide variety of boundary condition combinations, in this study, the method is used for evaluating the modal characteristics of an all edges free plate. Acoustic pressure levels are calculated by Rayleigh's acoustic formula for a free field. This study provides a quick formula for those who are interested in calculating the sound pressure of a baffled plate on a specific point for a free field while only requiring the vibration of the surface to be expressed in terms of 2D power series. The results obtained from the formula are compared with the finite element analysis results. (C) 2022 Institute of Noise Control Engineering.