Provided are a flexible display panel and a flexible display device, in which a non-display area surrounds a display area. A concave area protrudes along a direction away from interior of display area. A convex area has a folding axis parallel to a first edge. The non-display area includes a fan-out area, in which lead wires are provided. Each lead wire has a first end and a second end. There are signal traces each extending along a first direction provided in display area. The signal traces are electrically connected to first ends of lead wires. The convex area and concave area are arranged along a second direction. The second direction intersects first direction. A driving chip is included, which is a ball grid array package driving chip and is arranged in concave area where lead wires are away from first edge and electrically connected to second ends of lead wires.