A sorting machine (1) for sorting flat articles on edge, which machine has sorting outlets (2) for stacking the sorted flat articles, each of which sorting outlets is equipped with a stacking actuator (5) and with at least one slide plate (4) having a front face (40) against which the flanks of the flat articles slide while the flat articles are being stacked, the sorting machine (1) being provided with a noise damper and reducer (8, 12) for damping and reducing noise generated by the flat articles while they are being stacked, at least a portion of the noise damper and reducer (8) being provided on the slide plate (4).