If a plane sheet (membrane of plate), which is excited by homogeneous random pressures, is assumed to be infinite in extent then a very direct method of analysis is possible. However, several important applications concern structures which are far from infinite in extent (e.g., the excitation of panels by boundary layer pressure fluctuations, and the problem of structural vibrations due to jet noise). This restriction may be overcome by using the method of normal modes, which is more cumbersome by its very nature. It turns out that if it is the power spectrum of displacement which is required, then the “infinite” approach can be used only when the sheet is large enough for there to be only negligible reflections from its edges. However, if one is concerned only with the average mean square value of displacement (or related quantities), and if the detailed shape of the spectrum is of no consequence, then the infinite solution may be used, regardless of the magnitude of the damping, provided that the gravest modes are not excited.