An optical fibre ribbon structure suitable for use in an optical cable or other application where there is a risk that optical fibres will be subjected to a tensile force comprises a plurality of optical fibres and flexible reinforcing elements of resilient material arranged side by side and embedded in an elongate plastics body. Each resilient reinforcing element is set in such a form that the ribbon structure follows a path of smoothly curved undulations whose axes of curvature lie parallel to one another and normal to the longitudinal axis of the ribbon structure. When the undulting ribbon stucture is subjected to a tensile force, the ribbon structure straightens in a lengthwise direction against the action of the resilient reinforcing elements thereby reducing the tensile force otherwise applied to the optical fibres. When the tensile force is removed, the ribbon structure returns towards its original undulating form.