Wires and cables are valuable components for the design of mechanical structures, due to their high strength-to-lightness ratio. Their efficiency is only guaranteed when they are subjected to tensile stress: indeed, they exhibit a unilateral behaviour with a lack of stiffness in compression. The tensile state depends on the distribution of stress through the whole structure. The computation of this stress state requires to deal with nonsmooth relations arising from the modelling of the unilateral behaviours, leading to specific numerical strategies. Two examples of such structures are investigated. Tensegrity structures are light reticulated systems composed of bars in compression and a large number of tensioned cables. As poetically defined by Fuller [1], they are viewed as “islands of compression in an ocean of tension.” TexSol is a reinforced geomaterial made of sand and wires. This type of material is adapted for the embankments requiring a strong slope or works which may be subjected to a dilatation strain. In this case, the nonsmoothness is not reduced to the wire behaviour but concerns as well the frictional contact between grains and between grains and wires.