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The electromagnetic response of a multiwall carbon nanotube (MWNT) of small cross-sectional radius and finite length was theoretically studied in the terahertz and sub-terahertz regimes, by solving an integral equation. The polarizability of the MWNT peaks in the terahertz regime, depending on the length and the number of metallic shells. At lower frequencies, a strong depolarizing field creates a shielding effect: the penetration depth of the axial component of incident field depends on the frequency, the length, and the electron relaxation time. The screening effect makes MWNTs promising as interconnects.