Carbon nanotubes (CNT) posses a very large application potential in the rapid developing field of molecular electronics. Infinite single-wall metallic CNTs have theoretically a conductance of 2×G₀, (G₀ = \frac2e²h) 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 contacts. We study electron transport in single- and double-wall CNTs contacted to metallic electrodes with a fcc(111) surface within the Landauer transport formalism combined with Green function techniques. The electronic structure of the CNTs is described with a simple p-orbital model.We show that the symmetry of the contact region may lead in some cases to blocking of one of the transport channels reducing the conductance to 1×G₀ for single-wall CNTs. In the case of double-wall systems with both inner and outer shells being metallic, non-diagonal selfenergy contributions from the electrodes may induce mixing of the CNT's channels, again reducing the conductance from the theoretically expected value (4×G₀). Finally, we discuss the influence of inter-wall interactions on the conductance.