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Mathematical modeling is one of the leading methods for analyzing and predicting the dynamics of soil organic matter. Currently, only a few biogeochemical models incorporate the concept of soil carbon saturation, which assumes that soils have a limited ability to stabilize organic carbon as a result of interaction between organic matter and mineral particles. In this paper, we discuss the results of modeling based on the minimal SOCS (Soil Organic Carbon Saturation) model reflecting the saturation concept to better understand and assess how the limited ability of soils to stabilize organic matter affects its dynamics. To implement the model, we use the TerM (Terrestrial Model) universal constructor of models of the carbon cycle in soil and vegetation, designed by the Institute of Numerical Mathematics of the Russian Academy of Sciences–Moscow State University for the numerical experiments simulating the land’s active layer. Chernozems and Albic Retisols under natural vegetation and arable land of the European Russia are the objects of our study. The model parameters have been estimated for the upper mineral soil layer. The calculations using a quantitative assessment of the maximum capacity of mineral soils with a twofold prevalence of highly active minerals 2 : 1 to store carbon (87 mg C/g <50-µm fraction) show that the degree of carbon saturation defined as the ratio of the content of mineral-associated organic matter (MAOC) to the maximum observed mineral capacity in meadow-steppe chernozems and forest soddy-podzolic soils is 49.4 and 16.8%, respectively. In arable chernozems, this degree decreases to 42% and in arable soddy-podzolic soils, to 11.5%.