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The damping effect that is observed when a fibrous acoustical treatment is applied to a thin metal panel typical of automotive structures has been modeled by using three independent techniques. In the first two methods the fibrous treatment was modeled by using the limp frame formulation proposed by Bolton et al., while the third method makes use of a general poro-elastic model based on the Biot theory. All three methods have been found to provide consistent predictions that are in excellent agreement with one another. An examination of the numerical results shows that the structural damping effect results primarily from the suppression of the nearfield acoustical motion within the fibrous treatment, that motion being closely coupled with the vibration of the base panel. The observed damping effect is similar in magnitude to that provided by constrained layer dampers having the same mass per unit area as the fibrous layer.