This paper applies ideas originally developed in the field of acoustics of multiscale porous media to the analytical modeling of dissipative silencers. Analytical models for the long-wavelength acoustical properties of different types of dissipative silencers, such as pod silencers, lined ducts, splitters, and bar silencers, are introduced in this work. Some of these models account for the possibility of using different porous materials in a given silencer. For instance, a model for a splitter silencer comprising baffles made of different porous materials is derived. Examples of the sound transmission behavior of the said types of silencers are presented to evidence that the dissipation of sound energy is largely influenced by pressure diffusion occurring in the porous constituents. The predictions of the analytical models are in good agreement with finite element calculations.