A stacker device (1) for stacking flats (100) on edge, which device includes a stacking support (2) that extends along a certain stacking axis (D2) for storing flats (100) on edge and in a stack, which flats are inserted successively onto said stacking support (2), a stacking actuator (4) for guiding each flat (100) to be stacked along an insertion axis (D1) transverse to the stacking axis (D2), and for inserting it at the back of said stack of flats (100), said stacking support (2) being mounted to move relative to the stacking actuator (4) along the stacking axis (D2), and said stacker device (1) including impulse means (9) synchronized with the stacking actuator (4) so as to move the stacking support (2) in translation by applying an impulse along the stacking axis (D2) when a flat (100) is inserted at the back of said stack of flats (100). A storage device and a postal sorting machine including such a stacker device (1).