The acoustic design of exhaust mufflers has mainly focused on reducing the discharge noise from the tailpipe. However, the noise that is transmitted through the muffler jacket and the endplate becomes important since the muffler reduces the amount of discharge noise when it has an optimized design. It is known that the contribution to the overall exhaust noise of the muffler shell is significant in the mid- and high-frequency ranges. The current problem is that there are no appropriate computational tools at high frequencies. A simple method to analyze the 1/3-octave band of sound radiating from an arbitrary shape (like a muffler) was employed to predict the band spectrum of the radiated noise. The calculation method included formulating the boundary integral, which was modified into a quadratic form in order to enable the prediction of the intensity levels in a band analysis. Monopole and dipole source terms in the conventional BEM were transformed into the auto- and cross-spectra of the two vibrating sources, in which the cross-spectra could be eventually omitted by assuming that the correlation coefficients were negligible. The method was adopted in an abrupt calculation of the shell noise in 1/3-octave band levels without nonuniqueness problem. In comparison with the measured data, the simulation result showed roughly 3-dB errors at most of the field points, excluding several special points that were normal to the shell and exhibited a maximum 5-dB error.