We develop in this paper a theoretical approach to describe the electrodynamics of carbon nanotubes (CNTs). A lattice dynamics formalism is employed to model the mechanical response of matter to the radiation field. We start first by deriving the normal modes of the free lattice. Then, a simple and general microscopic model for light-matter interaction is proposed and the resulting mechanical equation of motion is derived using a suitable Lagrangian formalism. The symmetry group of the CNT is

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... ployed to explicitly probe the nonlocal structure of the fields and to carefully insure that higher-order Floquet modes are included in the derivation. The normal modes are then employed to perform an eigenmode expansion for the solution of the mechanical equation of motion, leading to the susceptibility tensor of the CNT medium. The final expression of this tensor describes the electrodynamics in the CNT viewed as a low-dimensional surface and is shown to be reduced effectively to a one-dimensional response function.