Using first principles theory based on density functional formulation we have studied the energetics and thermal stability of storing hydrogen in B−N-based nanostructures. We show that hydrogen molecule enters through the hexagonal face of the B 36 N 36 cage and prefers to remain inside the cage in molecular form. The energy barriers for the hydrogen molecule to enter into or escape from the cage are respectively 1.406 eV and 1.516 eV. As the concentration of hydrogen inside the cage increases, the cage expands and the bond length of the hydrogen molecule contracts, resulting in significant energy cost. At zero temperature, up to 18 hydrogen molecules can be stored inside a B 36 N 36 cage corresponding to a gravimetric density of 4 wt %. However, molecular dynamics simulation by using Nose algorithm at room temperature (T = 300 K) indicates that high weight percentage hydrogen storage cannot be achieved in B−N cage structures and thus these materials may not be good for practical applications.