The mechanism and dynamics of the formation of a hydrogen molecule by incorporating two hydrogen atoms in a stepwise manner into the cavity of some POSS (polyhedral oligomeric silsesquioxanes) compounds has been investigated by ab initio molecular orbital and ab initio molecular dynamics (AIMD) methods. The host molecules in the present reactions are two types of POSS, T-8 ([HSiO1.5](8)) and T-12(D-2d) ([HSiO1.5](12)). AIMD simulations were performed at the CASSCF level of theory, in which two electrons and two orbitals of the colliding hydrogen atoms are included in the active space. The trajectories were started by inserting the second hydrogen atom into the hydrogen atom-encapsulated-POSS (H + H@T-n -> H-2@T-n; n = 8 and 12). In many cases, the gradual formation of a hydrogen molecule has been observed after frequent collisions of two hydrogen atoms within the cages. The effect of the introduction of an argon atom in T-12 is discussed as well.