Rectangular, thin plates are common structural elements employed in many engineering applications and are subject to a wide variety of excitations, including acoustic excitations. This article analyses the deflection of an isotropic rectangular clamped thin plate. An exact solution of the governing equation of the problem is given in the form of a double series expansion in terms of a set of orthogonal functions. Furthermore, a simple and efficient finite element for thin-plate bending applications is also used. Numerical solutions for rectangular plates with various side ratios are presented and compared to the previous results and the finite-element analysis.