As the importance of sound attenuation through weight-critical structures has grown and mass law based strategies have proven impractical, engineers have pursued alternative approaches for sound attenuation. Membrane-type acoustic metamaterials have demonstrated sound attenuation significantly higher than mass law predictions for narrow, tunable bandwidths. Similar phenomena can be achieved with plate-like structures. This paper presents an analytical model for the prediction of transmission loss through rectangular plates arbitrarily loaded with rigid masses, accommodating any combination of clamped and simply supported boundary conditions. Equations of motion are solved using a modal expansion approach, incorporating admissible eigenfunctions given by the natural mode shapes of single-span beams. The effective surface mass density is calculated and used to predict the transmission loss of low-frequency sound through the plate–mass structure. To validate the model, finite element results are compared against analytical predictions of modal behavior and shown to achieve agreement. The model is then used to explore the influence of various combinations of boundary conditions on the transmission loss properties of the structure, revealing that the symmetry of plate mounting conditions strongly affects transmission loss behavior and is a critical design parameter.