Abstract. The article presents the results of studies confirming the law of the gamma distribution of microcapillaries in the structure of materials having a stochastic structure, for example, natural skins. The relative humidity of the latter depends on the mass of moisture collected by the microcapillaries, with heat and mass transfer under vacuum conditions. Numerical values of relative humidity in this case may differ from those recommended by footwear manufacturing technologies and should be considered as an integral part of the phenomenon of high-intensity heat and mass transfer under vacuum conditions and be determined by the proposed models.