Principles of the mathematical description of the grinding process have been developed which make use of linear models of population balance and substitute for the real distribution of the time of grain processing inside the mill a combination of ideal extrusion and ideal mixing. A convenient feature of these models is the use of equations with discrete distribution of grinding product grain size. The authors present these equations, which model the process of grinding in a ball mill disregarding the influence of a spiral classifier usually operating with a mill in a closed cycle. The authors also describe the mathematical model of a spiral classifier. Characteristics of product grain size classes and specific trituration rates for a closed cycle are shown for different procedures.