Method of producing compound curved surfaces, consisting of the step of rounding (ARC) with a radius R at an intersecting portion between a first linear approximated curved line (11) on a first three-dimensional curved surface (1) and a second linear approximated curved line (12) on a second three-dimensional curved surface (2) so as to produce a compound curved surface. Out of segments (Pi Pi-l) constituting the first curved line (11), and segments (Pj Pj+l) constituting the second curved line (12), one segment which is nearest to the intersection (PO) of these curved lines is selected from these curved lines successively. These two segments (PiPi-l, Pj Pj+l) are then checked whether there exists the arc of radius of R, which is tangent to said segment. When there is such an arc, it is inserted into the intersecting portion between the curved lines (11, 12) to round the intersecting portion. However, when there exists no such an arc, segments which are next nearest to the intersection (PO) are selected, and the same process as mentioned above is repeated to insert the arc into the intersecting portion to thereby round the same.