A sheet storing apparatus, comprising: a casing which is substantially rectangular parallelepiped and in which an upper unit and a lower unit are housed in such a manner that the upper unit and the lower unit can be each pulled forward from a front surface of the casing, the lower unit having a sheet storing mechanism provided inside the lower unit, wherein the sheet storing mechanism comprises: a pair of holding members for mounting a bag, wherein the pair of holding members is configured to hold parts facing each other of an opening portion of the bag, and a sheet feeding section configured to feed the sheets to the bag holdable by the holding members, the sheet storing apparatus further comprising: a compression section configured to perform first compression in a vertical direction and second compression in the vertical direction after the first compression by applying a pressing force to sheets storable in the bag, wherein the compression section comprises a stage configured to support the sheets storable in the bag from below via the bag and a pressing plate applying the pressing force to an upper surface of the sheets storable in the bag; and a control section configured to control the pressing force and to cause the compression section to be lowered while the second compression is performed, wherein when the compression section performs the first compression, the compression section applies a first pressing force to the sheets storable in the bag, and when the compression section performs the second compression, the compression section applies a second pressing force that is smaller than the first pressing force to the sheets storable in the bag, wherein during the second compression, the pressing plate and the stage are lowered simultaneously until the lower surface of the pressing plate reaches a target position, and the stage moves a distance that is larger than a distance of the movement of the pressing plate. a casing which is substantially rectangular parallelepiped and in which an upper unit and a lower unit are housed in such a manner that the upper unit and the lower unit can be each pulled forward from a front surface of the casing, the lower unit having a sheet storing mechanism provided inside the lower unit, wherein the sheet storing mechanism comprises: a pair of holding members for mounting a bag, wherein the pair of holding members is configured to hold parts facing each other of an opening portion of the bag, and a sheet feeding section configured to feed the sheets to the bag holdable by the holding members, a pair of holding members for mounting a bag, wherein the pair of holding members is configured to hold parts facing each other of an opening portion of the bag, and a sheet feeding section configured to feed the sheets to the bag holdable by the holding members, the sheet storing apparatus further comprising: a compression section configured to perform first compression in a vertical direction and second compression in the vertical direction after the first compression by applying a pressing force to sheets storable in the bag, wherein the compression section comprises a stage configured to support the sheets storable in the bag from below via the bag and a pressing plate applying the pressing force to an upper surface of the sheets storable in the bag; and a control section configured to control the pressing force and to cause the compression section to be lowered while the second compression is performed, wherein when the compression section performs the first compression, the compression section applies a first pressing force to the sheets storable in the bag, and when the compression section performs the second compression, the compression section applies a second pressing force that is smaller than the first pressing force to the sheets storable in the bag, wherein during the second compression, the pressing plate and the stage are lowered simultaneously until the lower surface of the pressing plate reaches a target position, and the stage moves a distance that is larger than a distance of the movement of the pressing plate. a compression section configured to perform first compression in a vertical direction and second compression in the vertical direction after the first compression by applying a pressing force to sheets storable in the bag, wherein the compression section comprises a stage configured to support the sheets storable in the bag from below via the bag and a pressing plate applying the pressing force to an upper surface of the sheets storable in the bag; and a control section configured to control the pressing force and to cause the compression section to be lowered while the second compression is performed, wherein when the compression section performs the first compression, the compression section applies a first pressing force to the sheets storable in the bag, and when the compression section performs the second compression, the compression section applies a second pressing force that is smaller than the first pressing force to the sheets storable in the bag, wherein during the second compression, the pressing plate and the stage are lowered simultaneously until the lower surface of the pressing plate reaches a target position, and the stage moves a distance that is larger than a distance of the movement of the pressing plate.