Embodiments of the present invention provide methods and apparatuses that can control rigidity of a flexible display. Embodiments of the present invention enable a user of the flexible display to control rigidity of the flexible display based on user preference, sensing information, program instruction, or combinations thereof. Embodiments of the present invention provide several ways to control rigidity of the flexible display by manipulating one or more rigidity control members disposed on the flexible display. Accordingly, embodiments of the present invention provide a way to allow the flexible display to have varying rigidity throughout portions of the flexible display.