A covering device for applying an elastic cover to an elongate object includes a folded elastic sleeve having an inner sleeve portion and at least one coaxially disposed outer sleeve portion overlaying the inner sleeve portion. The inner and outer sleeve portions are continuously joined at least at one circumferential edge. The folded elastic sleeve is positioned on a support for holding the folded elastic sleeve in a radially stretched condition. The support has a first end arranged adjacent to the continuous joint of the outer and inner sleeve portions. Relative movement between the outer sleeve portion and the inner sleeve portion results in the outer portion moving and recovering onto the elongate object. The support includes stress relief means associated with the first end for reducing the stress in the outer sleeve portion adjacent the first end of the support when the outer sleeve portion has been moved onto the object to be covered.
