Effects of zeolite support on reactivity of Pd-4 cluster toward dihydrogen molecules were studied at the DFT level using T6 (six-ring) and T24 (sodalite cage) clusters as models of zeolite FAU. It has been found that Pd-4 cluster binds to O-centers of T6 cluster via eta(3) and eta(2) coordination modes, leading to three different T6/Pd-4 clusters. For the energetically most stable triplet state T6/Pd-4 structures, the energy of interaction between Pd-4 and the constrained T6 ring is calculated to be ca. -5 kcal/mol. Encapsulating Pd-4 in a sodalite cage (T24) with the full relaxation of cluster geometry resulted in the Pd-4-zeolite interaction energy of -7.4 kcal/mol after correcting for basis set superposition error. The H-H bond activation barrier associated with the first H-2 addition to the triplet state T6/Pd-4 clusters (Delta E-0/Delta H, kcal/mol) varies from (2.2/0.7) to (3.2/2.0) to (4.8/3.5), depending on the path. Comparison of the calculated H-2 addition barriers for the T6-supported and gas-phase Pd-4 indicates that embedding of Pd-4 on zeolite reduces this barrier slightly (by 1.8/2.1 kcal/mol). Interestingly, the characteristic gas phase Pd-4-H-2 active site structural motif has been preserved in the T6-supported transition state structures. The heat of the reaction of the addition of first H-2 to the triplet state T6/Pd-4 ranges from (-17.6/-18.9) to (-21.8/-23.5) for the paths considered. The addition of the second, third and fourth H-2 molecules to the respective first H-2 addition products leads to the dissociative addition product only for the continuation of the single first H-2 addition path.