A polygon motor consists of several mirror faces and it is one of the core components for laser beam printers and copiers. Under high-speed rotation, aeroacoustic noise with a peak frequency of rotational speed times the number of mirror faces and its harmonics is prominently generated from a polygon motor covered with a casing. This paper describes a method to predict such noise that is generated from the flow, between the rotating mirror and stationary casing that propagates through the casing and is radiated into the ambient air. The unsteady flow is first computed by large-eddy simulation. The computed pressure fluctuations on the inner wall of the casing are then fed to structural analysis based on a dynamic explicit finite element method that computes the propagation of the elastic waves in the casing. Resulting external surface velocities are finally used for the computation of the acoustical field. A good correlation between the computed and measured results has been observed both in terms of velocity spectra on the casing and the spatial distribution of sound pressure level. The proposed method thus seems a promising engineering tool for predicting and identifying the generation mechanism of such noise that is generated from unsteady flow that propagates through solid walls and is radiated to ambient air, in general.