The anisotropic properties of phyllosilicate rocks are investigated through the modeling of the pore-free "intrinsic" elasticity of a textured muscovite aggregate. The elastic constants were calculated for textures, as defined using orientation distribution functions (ODFs), ranging from perfectly aligned to completely random. The ODFs were described using a Gaussian distribution, the width of which is controlled by the standard deviation of the orientations of the crystal c axis with respect to the sample foliation plane under the assumption that the sample has hexagonal (transversely isotropic) symmetry. The values were obtained using the widely used Voigt-Reuss-Hill averaging techniques as well as the geometric mean average (GMA). The GMA is more physically meaningful in that it requires that the elastic constants determined in either the stiffness or the compliance domains be invertible. Comparisons between these different averages indicate that, strictly, the Voigt and Reuss values do not necessarily provide the limiting bounds as is expected for the isotropic case. Despite this, some characteristics of the elastic wave P wave anisotropy are only weakly dependent on the averaging procedure employed. The calculated elastic constants are converted to the anisotropic $varepsilon$, δ, and γ parameters in order to allow for comparison to existing measurements in the literature. However, these "intrinsic" results are not intended to provide a measure of the properties of phyllites per se but to provide a reference against which more sophisticated models that incorporate porosity, layering, and composition may be constructed.