A sheet stacking apparatus which is capable of efficiently stacking sheets of various sizes while efficiently using space therein to thereby realize compactness thereof, and maintaining a high availability. Stacker trays for stacking sheets discharged from an image forming apparatus can be separately removed. It is detected whether any of the stacker trays is removed. When large-size sheets are stacked, a stacker control section causes the stacker trays to operate as one tray to stack the sheets in a state extending on the stacker trays, whereas when small-size sheets are stacked, the section causes one of the stacker trays to stack the sheets. Further, when one stacker tray is removed to make it impossible to stack the large-size sheets, the section causes a display section to display a guide message advising setting of the removed stacker tray.