The folding machine has a cross fold module which includes a cross-fold folding blade (18), a sheet-supporting device (38) which is arranged below the cross-fold folding blade (18) and on which an incoming sheet comes to rest, and a roller frame (27) which is arranged below the sheet-supporting device (38) and into which a sheet is introduced by the cross-fold folding blade (18). A three-fold module (22) with a three-fold folding blade (24) arranged perpendicularly with respect to the cross-fold folding blade (18) is arranged downstream of the roller frame (27). The three-fold module (22) and the roller frame (27) are arranged on a rotary stand (20) which is rotatable through at least 180 about a vertical axis (28).