There are provided a sheet stacking apparatus capable of stably stacking a large number of sheets and an image forming apparatus. The sheet stacking apparatus configured to stack sheets includes a plurality of discharge units disposed to an apparatus main body in a vertical direction and configured to discharge sheets, a plurality of sheet stacking units disposed to be independently elevatable on a side surface of the apparatus main body corresponding respectively to the plurality of discharge units and configured to stack thereon the sheets discharged from the discharge units, and an alignment unit disposed between the plurality of sheet stacking units and configured to sequentially align a position in a width direction perpendicular to a discharging direction of the sheets stacked on a lower sheet stacking unit among the plurality of sheet stacking units.