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Abstract.A description of five mathematical models of the water-retention capacity of soil is given, taking into account the hysteresis phenomena. A computational experiment was carried out with these models using data on sandy soil. The experiment consisted of: (i) tuning of the models (parameter identification) by the method of dot-approximation of experimental data on the main drying and wetting branches of the hysteresis loop using an optimizing algorithm; (ii) the predictive calculation of the scanning branches of the hysteresis loop; (iii) a comparison of the errors in tuning results and the predictive calculation using the Williams-Kloot criteria. The commensurate and sufficiently low errors in the adjustment of the models have been achieved. The differences in the calculation of the scanning hysteresis branches are revealed. The practical significance of the mathematical models presented is to ensure the calculation of precision irrigation rates. The application of such rates in irrigation farming will help to prevent excess moisture from flowing beyond the root layer of the soil under the influence of gravity and, thus, to minimize the losses (unproductive consumption) of irrigation water, fertilizers, meliorants and plant protection products, and also reduce the risk of groundwater contamination with agrochemicals and eutrophication of water bodies.