At low porosity, the elastic moduli of the rock mineral matrix often dominates those of the whole rock. A sedimentary rock matrix may be considered as a composite and may include mineral constituents with very different moduli and shapes. To describe the fabric of these rocks, an unmanageable number of parameters may be needed. Understanding the elastic behavior of synthetic composites, which are easier to model, enables us to quantify the effect of each parameter on the elastic moduli of the rock matrix independently. We test whether the differential effectivemedium (DEM) and self-consistent (SC) models can accurately estimate the elastic moduli of a complex rock matrix and compare the results with the average of upper and lower Hashin-Shtrikman bounds (HS). The testing was conducted using data from the literature on composites, covering a wide range of inclusion concentrations, inclusion shapes, and elastic modulus contrasts. We find that when the material microstructure is consistent with the DEM approximation, DEM is more accurate than both SC and the bound-average method for a variety of inclusion aspect ratios, concentrations, and modulus contrasts. If relatively little information is known about the rock microstructure, DEM can estimate the elastic properties of complex mixtures of minerals more accurately than heuristic estimates, such as the arithmetic average of the upper and lower elastic bounds.