The invention provides a capacitive touch type flexible display panel and a flexible display thereof, wherein the capacitive touch type flexible display panel comprises a touch display area and a bending induction area; the bending induction area surrounds the touch display area; a plurality of induction electrodes are arranged in the touch display area; a plurality of induction units are arranged in the bending induction area; the plurality of induction units and the plurality of induction electrodes are connected with a touch chip; and the touch chip corrects capacitance values measured by the plurality of induction electrodes according to screen body bending position information sensed by the plurality of induction units. In the capacitive touch type flexible display panel and the flexible display thereof provided by the invention, the induction units are arranged around the touch display area; therefore, the screen body bending position is sensed; capacitance correction values are fed back to the touch chip; and thus, error judgement of a touch signal is reduced.