Prospects for the application of advanced composites in the offshore technology of oil production are considered. The use of composites in vertical pipelines-risers seems to be the most efficient. The operating loads are studied and the attendant problems are formulated. A comparative analysis of the characteristics of metal, composite, and metal-composite deep-water risers is presented. A technique is developed for designing multilayered risers, taking into account the action of internal and external pressures, gravity, and the axial tensile force created by tensioners, as well as the residual technological stresses due to the difference in coefficients of thermal expansion, physical-chemical shrinkage, and force winding. Numerical estimations are given for a two-layered riser with an inner metal layer of steel, titanium, or aluminum alloys and a composite layer of glass- or carbon-fiber plastics formed by circumferential winding. It is shown that the technological stresses substantially affect the characteristics of the riser.