The paper describes the study of the kinetics of filtration drying of barley brewer’s spent grain. The dependencies of the process at different parameters of the stationary layer and the heating agent are presented: different heights of the wet material H (40 mm, 80 mm, 120 mm, and 160 mm), different temperatures of the heating agent T (50 °C, 70 °C, 80 °C, and 90 °C), and the velocities of the heating agent through the stationary layer of material v0 (1.26 m/s, 1.55 m/s, 1.81 m/s, 2.31 m/s, and 2.82 m/s). The kinetic regularities of two drying periods were determined: the period of complete saturation of the heating agent with moisture and the period of partial saturation of the heating agent with moisture. The calculation dependencies describing the intensity of the filtration drying process in both periods are proposed. The equations for determining the drying time of barley brewer’s spent grain τI and τII during both periods are proposed. The absolute value of the maximum relative error of the experimental values of moisture content from the theoretically calculated ones is 19.83 %, and the average value of the relative error is 3.15 %, which is acceptable for practical design calculations of drying equipment.