A flexible display apparatus and a control method therefor. The flexible display apparatus comprises: a flexible display panel (10); a bending sensor (11), that is configured to sense bending information of the flexible display panel (10); and a processor, that is coupled to the bending sensor (11), configured to receive the bending information of the bending sensor (11), and determines whether the bending information is valid bending information, and if so, then a currently running application program is controlled according to the valid bending information to perform a corresponding operation. By bending the flexible display panel (10), an application program is controlled to perform a corresponding operation, achieving a convenient, accurate, and effective operation, and improving user experience.