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In the present work, fully clamped rectangular isotropic plates are investigated: the response under steady-state excitation determined by harmonic point force application is calculated, and the consequent sound radiation is evaluated. The study is carried out both analytically and numerically. At first, the analytical solution of the clamped-clamped plate motion equation is calculated by means of a MATLAB implementation. The solution is based on the Principle of Virtual Work, calculating the displacement as a function of frequency at the nodes of a rectangular mesh. The monopole approximation of Rayleigh’s integral is then used to estimate the sound radiation in free field propagation. The numerical solution is evaluated using COMSOL Multiphysics, employing the Finite Elements Method (FEM). The clamped plate is modeled as a shell and “Acoustic-Structure Boundary” coupling is employed.