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In this paper, experimental evidence will be presented to demonstrate that unstiffened, low density fibrous materials are “limp”: i.e., their in vacuo bulk stiffness is very small compared to that of air with the result that the materials' solid phase motion becomes acoustically significant. Next, a new limp porous material model is presented. It is shown that this model may be used in conjunction with transfer matrices to predict the absorption or transmission loss of arbitrarily layered combinations of fibrous layers, permeable or impermeable membranes, and air spaces. The predictions of this model agree well with experimental measurements and so may be used to optimize sound absorption or transmission treatments.