The toxicity of inclusion compounds formed by carbon nanostructures depends on its functionalized surface, use of solvents, dosage and other properties. Molecular modeling has potentially contributed to the understanding of the chemical nature of the formation of these systems and allows advancement in studies of the mechanism of transport, release of drugs and their biological implications. This work reports a quantum chemical investigation of the inclusion complexes formation between oxidized carbon nanotube (CNTox)/nanocone (CNCox) structure and cisplatin molecule, using the density functional theory (DFT) with the B3LYP functional and 6–31G(d,p)/LanL2DZ standard basis sets. Our results indicate that the cDDP@CNTox (inclusion complex – cisplatin into oxidized carbon nanotube) and cDDP@CNCox (inclusion complex – cisplatin into oxidized carbon nanocone) systems form stable molecular complexes that can be used as drug delivery devices. Our theoretical simulation of molecular spectra (IR, Raman and 1H NMR) reveals substantial changes due to complex formation that can be easily experimentally observed.