The two ways of theoretical determination and modeling of the elastic properties of geological or modern technological materials are discussed. Such samples are characterized by a whole string of parameters or distributions (volume parts of the phases, sizes, shapes of the grains, or voids and their orientations etc.). The direct way uses first principles, averaging the strain field calculated by FEM techniques. The indirect way, without absolute spatial characteristics, uses distributions averaging the single-crystalline elastic properties, supposing infinite samples with ideal disorder and non-overlapping. space filling units. Overlapping can effectively been simulated by the DEM technique. The (GeoMixSelf) GMS-approximation able to consider ellipsoidal units, including voids, combines elements of the geometric mean and the self-consistent approximation. One example demonstrates the potentials, limitations and possible combinations of both ways .
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