The object of the study reported here is the grinding process in a tumbling mill where the mechanism of destruction by crushing is implemented, which is caused by the mechanism of compression loading. The compressive interaction in the active zone of the lower end of the granular loading chamber of the rotating drum at the transition of the shear layer to the solid zone was taken into account. The task to determine the parameters of the compressive action was solved, which was caused by the difficulties of modeling and the complexity of the hardware analysis of the behavior of the internal loading of the mill. A mathematical model was built based on data visualization for the compression grinding mechanism. The power of compressive forces was taken as an analog of grinding performance. The initial characteristic of compression was considered to be the mean speed of movement in the central averaged normal cross-section of the shear layer. The influence on the performance of the mass fraction of the shear layer and the reversibility of loading was taken into account. The effect of rotation speed on productivity was evaluated by experimental modeling at a chamber filling degree of 0.45 and a relative size of grinding bodies of 0.0104. The maximum value of energy and grinding productivity was established at a relative speed of rotation ψω=0.6–0.65. The maximum value of the share of the shear layer loading was found at ψω=0.4–0.45. The results have made it possible to establish a rational speed during crushing by compression, ψω=0.55–0.65. This value was smaller in comparison with impact crushing, ψω=0.75–0.9. The observed effect is explained by the detected activation for the shear loading layer during slow rotation, in contrast to the fast rotation for the drop zone. The model built makes it possible to predict rational technological parameters of the process of medium and fine grinding in a tumbling mill by compression.