Materials compress each other in a directional material flow, causing energy and momentum to overflow. Materials moving at a low velocity outside the boundary of a rigid moving component form a finite dissipation zone. A discrete element model is established to explore its characteristics. First, the mass of material driven by the disk increases linearly with an increase in the translation distance, and the mass of material moving at a low velocity increases significantly. Second, the movement state of materials depends on its distance from the disk. The material velocity at the boundary of the finite dissipation zone is verified to be 1 mm/s by analyzing the material velocity and contact force. When the operating parameters are different, the boundary curves of the finite dissipation zone are similar but the numerical values are different. Third, the maximum edge extends 0.7−3.0 mm beyond the boundary, and this value is linearly related to the translation velocity with little impact from the lowering depth. Studying the mechanism of finite dissipation zones contributes to forming an efficient directional material flow and the energy dissipation mechanism under a flexible constraint.