A flexible display apparatus and a method configured to display three-dimensional (3D) space is disclosed. The flexible display apparatus includes a display that is deformable and is configured to display three-dimensional (3D) image data, a sensor configured to sense deformation of the display, and a controller configured to display some of the 3D image data corresponding to the sensed deformation of the display. The method for controlling a flexible display apparatus with a display includes sensing deformation of a display, and displaying some three-dimensional (3D) image data corresponding to the deformation when the deformation is bending of the display.