A sheet stacking tray apparatus for receiving sheets discharged from an image forming apparatus such as a printer or copying machine. The sheets are correctly stacked, that is, without inclination or deviation. The tray apparatus according to the present invention is such that the speed at which the sheet is discharged to the tray apparatus is reduced when the tray apparatus receives the sheet material. And, the sheet is laterally shifted so as to correct the lateral deviation thereof. The tray is lowered in accordance with the amount of the sheets so as to keep a proper height thereof with respect to the discharging outlet from which it receives the sheet. An auxiliary sheet stacking plate is provided operable in association with the lowering of the tray so as to raise the sheet receiving side thereof so as to keep the sheet material on the tray horizontal.