A sheet processing apparatus capable of determining whether or not a press operation is to be performed on a folded part of a sheet bundle according to the number of sheets of the sheet bundle. If a folding priority mode is not set on a selection screen displayed on a display unit of the sheet processing apparatus, a controller of the sheet processing apparatus determines whether or not the number of sheets of the sheet bundle indicated in sheet bundle information is equal to or larger than a threshold value. The controller sets a press mode in the sheet bundle information to “press,” if the number of sheets of the sheet bundle is equal to or larger than the threshold value, and sets the press mode to “pressless,” if the number of sheets of the sheet bundle is less than the threshold value.