First principle quantum chemical calculations have been performed on a hydrogen molecule in the silicon crystal using the cluster model of Si10H16 The ab initio molecular orbital theory and the density functional theory (DFT) calculations have been examined. In all calculations, the tetrahedral site is the most stable trapping site for the hydrogen molecule. The DFT calculations with generalized gradient approximation show that the bond length of H-2 in the silicon crystal is comparable to that of gaseous H-2. The calculated vibrational frequency of H-2 in the silicon crystal agrees well with the experimental value obtained by Murakami et al. [phys. Rev. Lett. 77, 3161 (1996)].