A cover skin for a variable-shape aerodynamic area, such as a wing structure, tail unit structure, control surface structure or flap structure is described. A cover skin is deformable in one direction without exhibiting substantial deformation in a transverse direction. A deformable framework structure is embedded in a layer of an elastic material, such as rubber or polymer. The framework structure may be comprised of non-deformable elements joined pivotably in auxetic and non-auxetic assemblies of elements that are capable of substantially eliminating transversal contraction, when the cover skin is longitudinal stretched, and substantially eliminating transversal expansion, when the cover skin is longitudinally contracted.