A paper sheet processing machine configured to process a banknote, the paper sheet processing machine comprising: an identification unit configured to identify a banknote; a plurality of stacking units configured to stack banknotes based on details of a plurality of sort types identified by the identification unit; and a control unit configured to read an upper limit number of banknotes corresponding to details of the sort types of banknotes to be stacked in the stacking units from a storage unit storing the upper limit number of the banknotes to be stacked in the stacking units linked with the details of the sort types, and set the upper limit number of the banknotes to be stacked in the stacking units, wherein: the plurality of the sort types include a first sort type and a second sort type, the first sort type is fitness of a banknote, a detail of the first sort type of the banknotes includes a first type suitable for use in an external apparatus, a second type suitable for use other than the external apparatus, and a third type which is unusable, and the second sort type is a denomination of a banknote, characterized in that the storage unit stores the upper limit number of the banknotes to be stacked in the stacking unit linked with each of the plurality of details of the first sort type, when banknotes are stacked in two or more of the stacking units based on different details of the first sort type, the upper limit number of the banknotes to be stacked in each of the two or more of the stacking units is set based on the details of the first sort type, banknotes which are different from each other in detail of the first sort type, and are identical to each other in detail of the second sort type are stacked in the two or more of the stacking units, and an upper limit number of banknotes set for the first type is greater than an upper limit number of banknotes set for the second type and an upper limit number of banknotes set for the third type. an identification unit configured to identify a banknote; a plurality of stacking units configured to stack banknotes based on details of a plurality of sort types identified by the identification unit; and a control unit configured to read an upper limit number of banknotes corresponding to details of the sort types of banknotes to be stacked in the stacking units from a storage unit storing the upper limit number of the banknotes to be stacked in the stacking units linked with the details of the sort types, and set the upper limit number of the banknotes to be stacked in the stacking units, wherein: the plurality of the sort types include a first sort type and a second sort type, the first sort type is fitness of a banknote, a detail of the first sort type of the banknotes includes a first type suitable for use in an external apparatus, a second type suitable for use other than the external apparatus, and a third type which is unusable, and the second sort type is a denomination of a banknote, characterized in that the storage unit stores the upper limit number of the banknotes to be stacked in the stacking unit linked with each of the plurality of details of the first sort type, when banknotes are stacked in two or more of the stacking units based on different details of the first sort type, the upper limit number of the banknotes to be stacked in each of the two or more of the stacking units is set based on the details of the first sort type, banknotes which are different from each other in detail of the first sort type, and are identical to each other in detail of the second sort type are stacked in the two or more of the stacking units, and an upper limit number of banknotes set for the first type is greater than an upper limit number of banknotes set for the second type and an upper limit number of banknotes set for the third type. the plurality of the sort types include a first sort type and a second sort type, the first sort type is fitness of a banknote, a detail of the first sort type of the banknotes includes a first type suitable for use in an external apparatus, a second type suitable for use other than the external apparatus, and a third type which is unusable, and the second sort type is a denomination of a banknote, characterized in that the storage unit stores the upper limit number of the banknotes to be stacked in the stacking unit linked with each of the plurality of details of the first sort type, when banknotes are stacked in two or more of the stacking units based on different details of the first sort type, the upper limit number of the banknotes to be stacked in each of the two or more of the stacking units is set based on the details of the first sort type, banknotes which are different from each other in detail of the first sort type, and are identical to each other in detail of the second sort type are stacked in the two or more of the stacking units, and an upper limit number of banknotes set for the first type is greater than an upper limit number of banknotes set for the second type and an upper limit number of banknotes set for the third type.