A curling device and a flexible display device are provided. The curling device includes: the electromagnetic telescoping mechanism and the controller are in communication connection; the electromagnetic telescopic mechanism is configured to connect with the flexible display panel element and expanding under the action of the magnetic field when receiving a first signal of the controller so as to drive the flexible display panel element to expand; when a second signal of the controller is received, the flexible display panel element is curled, so that the flexible display panel element is driven to curl.