A gripping device for manipulating flexible elements includes a main rack and a plurality of gripping elements coupled in the main rack by respective operating mechanisms for gripping a flexible element. The gripping device includes at least four gripping elements for gripping the flexible element. At least one gripping element is a multiposition gripping element independently displaceable by a displacement system assembled in the main rack and a vertical operating mechanism. At least two of the other gripping elements are independently displaceable in any direction by respective two-way additional displacement systems assembled in the main rack. The gripping elements are automatically adjustable in their respective positions such that they are arranged in one and the same plane for capturing the flexible element in a flat two-dimensional configuration and movable to generate a three-dimensional configuration in the flexible element without generating stretching forces on the flexible element.