The selectivity of the bis(calix[4]arene)tetraethylene abbreviated as calix[4]tube for the endohedral complexation of alkali and alkaline earth metal ions, was predicted on the basis of structures and complex formation energies computed with three different quantum chemical methods: DFT LANL2DZp)/LANL2DZp), PM3/SPASS, and PM6. A comparison with published X-ray structures demonstrated that the most reliable results were achieved applying DFT calculations. The complexation of K⁺ and Ba²⁺ is most favorable, followed by the encapsulation of Rb⁺ and Sr²⁺, respectively. The flexibility of the tube, described by the torsion angles associated with the ethylene linkages between the calix[4]arene units and phenyl rings intersecting the plane of the four methylene carbon atoms, also makes an important contribution to its selectivity. In general, the cavity size is similar to [2.2.2] and [N2N2N2], the cryptands with the largest cavities previously studied in our group applying a similar protocol.