A sheet stacking system includes a main conveyor configured to carry sheets in a downstream direction, an accumulator section downstream of the main conveyor configured to receive the sheets from the main conveyor, at least one tamping plate in the accumulator section, and at least one linear motor connected to the at least one tamping plate. The at least one linear motor is configured to move the at least one tamping plate back and forth in a direction perpendicular to the downstream direction to tamp a stack of the sheets in the accumulator section.