Carbon nanotubes (CNT) posses a very large application potential in molecular electronic devices. Infinite single-wall metallic CNTs have theoretically a conductance of 2 X G₀(G₀=2e2/h) because of the two electronic bands crossing the Fermi level. For finite size CNTs experiments have shown that other values are also possible, indicating a very strong influence of the contact geometry. Here, electronic transport in single and double-wall CNTs contacted by metallic electrodes is studied by combining the Landauer transport formalism with Green function techniques. We demonstrate for some selected nanotubes that the symmetries of the CNT-metall interface may lead to a suppression of the conductance near the Fermi level below the theoretically expected value (2G₀ and 4G₀ for single and double-wall tubes, respecively). Finally, we also discuss the influence of inter-wall interactions on the conductance and find that it leads to a strong suppression of the transmission, mainly for energies not so close to the Fermi level.