Submerged cables and pipes, in 'catenary' configuration, are essential systems in offshore oil industry, particularly in deep-water exploration. The structural-mechanics behavior of this kind of system, in response to gravitational, hydrostatic, environmental loads and to motions imposed by the floating unit from which it is suspended, is inherentely non-linear. Geometric non-linearities, as those represented by the one-side constraint at the touchdown point, as well as hydrodynamic ones, are just few examples of such non-linear characteristics.This work treats the static configuration as well as the dynamic response problems.Emphasis is given to the study of curvature distribution in the extremities neighborhoods, either close to the touchdown point or to the suspension point, as those regions are critical, concerning design. The approach is analytical and experimental.The static problem is formulated and discussed under the classical theory of thin rods.The two-dimensional problem is analysed in depth. The effect of flexural rigidity is shown to be confined to small regions, close to the extremities, since no other intermediate restraint is supposed to exist, and classified as a standard singular perturbation problem in applied mathematics. The curvature in the touch-down point region is treated under the boundary-layer technique approach. An analytical solution is then constructed. The soil flexibility effect is properly incorporated and discussed.The analytical solution is compared to results of specifically conducted experiments, and validated. The boundary-layer technique is then applied to the curvature distribution in the upper end region, in the presence of a flexible end-fitting, and an analytical local solution is derived as well. A number of non-dimensional diagrams are presented and discussed under a designer perspective.