We have formulated a linear theory for the shielding effectiveness of composite matrix materials and have tested the theory for various amounts of ThermalGraph DKD X carbon fiber within nylon 6,6. The theory predicts that the most important parameters for the shielding effectiveness of a sample are the carbon-fiber volume percentage and the frequency of the wave to be shielded. Although we expected the model to be valid at low filler-loading levels, it actually performs remarkably, covering an electrical-resistivity range of 10(16) (at low filler-loading levels) to 10(1) Ohmcm (at high filler-loading levels), well above the percolation threshold of electrical-resistivity theory. The model performs much better than those reported in the literature and can be used to determine filler loadings needed to provide a certain level of shielding of electromagnetic waves. (C) 2005 Wiley Periodicals, inc.