Paper sheets, which are loaded in a supply section without any regard to which direction their first or second surface is facing, are supplied to a detecting section for checking as to whether the first surface is facing in a preselected direction and also for identifying the kind of paper sheet. The paper sheets supplied with their first surface facing in the preselected direction are sorted and stacked in first stacking sections in accordance with the kind of paper sheet. The paper sheets of all kinds supplied with their second surface facing in the preselected direction are stacked in a single second stacking section. Each of the paper sheets stacked in the second stacking section are supplied with their first surfaces facing in the preselected direction to the detecting section, again for identification of the kind, once again.