To define the asymptotic behaviour of elastic, one-dimensional structural elements, a vanishing parameter $(\varepsilon)$ is introduced, associated with the small elongations of high strength materials. Two categories of non linear problems are recognized, concerning respectively "rods" and "beams" according as the slenderness has the order $(\varepsilon)$ and $\sqrt{(\varepsilon)}$. First approximation formulations are presented for either case and refinements prospected.