A sheet processing apparatus that is capable of properly performing fold line processing at a position depending on a sheet bundle. In a sheet processing apparatus, sheets sequentially received from an image forming apparatus are stacked on a bookbinding processing tray to form a sheet bundle. The sheet bundle is folded at the center thereof, and is conveyed to a processing position. A press unit moves along a fold line portion of the sheet bundle to thereby perform flattening processing for flattening the fold line portion by pressing the fold line portion from a direction orthogonal to a thickness direction. A first pressing strength set by a user using the image forming apparatus and the second pressing strength acquired information on the sheet bundle are compared with each other, and the processing position is determined based on a result of the comparison.