Abstract <p>Development and modernization of equipment for processing bulk materials is a challenge that cannot be resolved without using adequate models of mixing processes. The paper presents a mathematical model of the mixing process in a new continuous-action drum-screw step mixer, which allows calculating the concentration fields of each component of the mixture in the working volume of the device. The model is based on a system of continuity equations for component concentrations. The shape of the volume occupied by the bulk mass in the steady-state mode of mixer operation and the fields of material movement velocity are modeled using simplified concepts based on experimental observations of the operation of gravity-driven drum-type mixers. When such mixers operate in the roll mode, the cross-section of the working volume occupied by the bulk material is divided into two zones. In the lower, transport zone, the material particles rise upward along the flow lines coinciding with the arcs of circles. In this case, the particles do not move from one flow line to another. Having reached the avalanche line, the particles enter the upper avalanche zone, where they enter the avalanche-like flow and roll down under the action of gravity, entering the transport zone again at the bottom of the avalanche line. In the presented model, it is assumed that the avalanche line coincides with a segment of the straight line inclined to the horizon at the avalanche angle of the bulk material. The model allows for mixture segregation and the effect of additional working elements—mixing blades—on the material flow. The concentration fields of the mixture components according to the proposed model can be calculated using known numerical methods for solving systems of partial differential equations.</p>