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The electronic structure and dielectric screening of finite-length armchair carbon nanotubes are studied within a tight-binding model, which well captures the oscillation pattern of the band gap as the tube length increases. We find that: (1) the parallel screening constant ε|| grows almost linearly with the length and shows little dependence on the band gap; (2) the perpendicular screening is strongly related to the band gap and ε⊥ converges to its bulk value when the length exceeds tens of radius. Our method is employed to study the depolarization effect of a short (6,6) nanotube in a wet environment, when water is inside the tube. This situation is of interest for biomimetic uses of carbon nanotubes.