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http://jap.aip.org/The randomness in the structure of two-component dense composite materials influences the scalar effective dielectric constant, in the quasistatic limit. A numerical analysis of this property is developed in this paper. The computer-simulation models used are based on both the finite element method and the boundary integral equation method for two- and three-dimensional structures, respectively. Owing to possible anisotropy the orientation of spatially fixed inhomogeneities of permittivity epsilon(1), embedded in a matrix of permittivity epsilon(2), affects the effective permittivity of the composite material sample. The primary goal of this paper is to analyze this orientation dependence. Second, the effect of the components geometry on the dielectric properties of the medium is studied. Third the effect of inhomogeneities randomly distributed within a matrix is investigated. Changing these three parameters provides a diverse array of behaviors useful to understand the dielectric properties of random composite materials. Finally, the data obtained from this numerical simulation are compared to the results of previous analytical work