This study aimed at perfecting the design theory of non-tube and non-tray folding carton, enriching design skills of interval structure and designing flexible carton to save paperboard materials. The structures of horizontal and oblique interval plates of non-tube and non-tray folding carton were studied by splitting and combining modes. This study put forward the directionality concept and pointed out the direction determining standards of the horizontal and the oblique interval plates. The horizontal cutting method and the oblique cutting method were directional and both unidirectional and bidirectional cuttings can form the carton. Design with directionality strengthened the theoretical support of carton structure design, enriched carton types and expanded the design ideas.