A theoretical method to study the encapsulation of H2 molecules in the cavities of Cs3Na9-A zeolite has been proposed. To study the properties of encapsulated H2 molecules, a Fermi-Dirac like statistics has been introduced. The average binding energy per H2 is obtained as a function of the number of molecules and temperature. The average activation energy is also calculated from the minimum energy path for the α- to α-cage transmission and the average binding energy. The fraction with higher energy than its activation energy has been calculated and revealed that the activation energy for the en- and decapsulation of H2 molecules depends not only on the temperature but also on the number of the encapsulated molecules.