A sheet stacking apparatus includes a stack unit which includes a first stack tray and a second stack tray which can be individually elevated and is configured to stack a sheet on at least one of the first stack tray and the second tray, and a control unit configured to control the stack unit to stack the sheet in a first stack mode in which the sheet is stacked on at least one of the first stack tray and the second stack tray without being extended over the first stack tray and the second stack tray and a second stack mode in which the sheet is stacked on across the first stack tray and the second stack tray, the control unit capable of selecting the first stack mode and the second stack mode with respect to a same size sheet.