Theoretical investigations have been carried out to explore the possibilities of Li+ ion intercalation or insertion through the side-wall or through the cap region of carbon nanotubes. Hartree-Fock(HF), MP2 and density functional (DFT) theories with minimal to extended basis sets were used to examine simple models of 5, 6, 7, and eight-membered-rings. The barrier to insert Li+ ion through these rings depends on the ring size. Insertion is easier as the ring size increases. Lithium ion favors two positions: (a) inside the tube close to the wall, and (b) outside of the tube. Energetic information is provided using simple models with different diameters. Movement of the cation(s) within a single-wall tube, in interstitial zone and within multiwall tube, are also studied and discussed.