A flexible display apparatus and control method thereof is provided. The flexible display apparatus may include a display, a sensor that senses one of a first deformed shape of the flexible display apparatus and a second deformed shape of the flexible display apparatus, and a controller which controls the display to display a first user interface (UI) corresponding to the first sensed shape in response to sensing the first shape and a second user interface corresponding to the second sensed shape in response to sensing the second shape, receives an input on the displayed UI, and transmits a control signal to a controlled apparatus that instructs the controlled apparatus to execute a function of the controlled apparatus corresponding to the input.