  In this paper we investigate the deformation of cylindrical linearly elastic
shells using the Koiter model. We formulate and solve the relaxed
Saint-Venant's problem for thin cylindrical tubes made of isotropic and
homogeneous elastic materials. To this aim, we adapt a method established
previously in the three-dimensional theory of elasticity. We present a general
solution procedure to determine closed-form solutions for the extension,
bending, torsion and flexure problems. We remark the analogy and formal
resemblance of these solutions to the classical Saint-Venant's solutions for
solid cylinders. The special case of circular cylindrical shells is also
discussed.
