In the current study, the density functional theory calculations (DFT) were employed to determine the hydrogen storage properties of some nanoclusters including C24, B12N12, Al12 N12, Be12O12, Mg12O12, and Zn12O12. After full geometrical optimization of all nanocages under the DFT framework, we found that C24 and B12N12 were unstable structures even in case of incorporating only one hydrogen molecule to them due to positive obtained formation energy magnitudes while Al12N12 and Be12O12 were able to adsorb one hydrogen molecules and became thermodynamically unstable for more than one hydrogen molecule. Also, Mg12O12 and Zn12O12 were capable of storing up to 4 hydrogen molecules according to negative achieved formation energies. Also, calculated bulk modulus revealed that when all studied structures stored H2 molecules the bulk modulus decreased compared to pristine nanoclusters. The highest reduction in bulk modulus was 10% which occurred in C24 while storing 5H2. Furthermore, the adsorption properties of these nanocages were considered using DFT and the results showed that Zn12O12 was a stronger adsorbent for H2 in comparison to the rest of the studied nanocages.