A paper sheet handling machine 1 comprises a casing 92 and at least two stacking units 30, 40 provided in the casing 92. Each stacking unit 30, 40 is configured to stack therein paper sheets respectively taken in the casing 92 by a take-in unit 10. From among the paper sheets transported by a transport unit 20, the paper sheets, each judged to be stored in the stacking unit 30 or 40 by a recognition unit 28, are diverted from the transport unit 20 and fed into the stacking unit 30 or 40, by each diverter 60, 62. A reject unit 50 is connected with the transport unit 20 on the downstream side of the diverters 60, 62. To the reject unit 50, the paper sheets that are not diverted from the transport unit 20 by the respective diverters 60, 62 are fed.