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The report is devoted to the practical application of the asymptotic averaging method for determining the effective elastic moduli and the Biot parameter of natural composites by the example of carbonate rocks (dolomites ['dɔləmaɪt] and limestones) and volcanogenic-sedimentary rocks (hyaloclastites). The results of the calculation coincided with the results of the experiment. The Biot parameter is difficult to determine experimentally. The averaging method makes it possible to calculate the tensor Biot parameter of the porous composites for the case of general anisotropy. The asymptotic homogenization method allows to investigate the dependence of elastic properties on porosity, shape and orientation of pores.