The structure and bonding nature of Pd(XH3)(eta(3)-C3H5)(PH3) (R-X; X = C, Si, Ge, Sn) and its C-X reductive elimination were investigated with MP2-MP4(SDQ) and CCSD(T) methods. The C-C reductive elimination is considerably exothermic (27.7 kcal/mol) and needs a significantly large activation energy (23.0 kcal/mol), where CCSD(T) values are given hereafter. This considerably large exothermicity can be easily interpreted in terms of the strong C-C bond and the weak Pd-CH3 bond. On the other hand, the C-Si, C-Ge, and C-Sn reductive eliminations easily occur with a moderate activation barrier (12-13 kcal/mol) and a moderate reaction energy; the exothermicities are 6.0 and 1.6 kcal/mol for the C-Si and C-Ge reductive eliminations, respectively, and the endothermicity of the C-Sn reductive elimination is 6.0 kcal/mol. These moderate reaction energies of C-Si, C-Ge, and C-Sn reductive eliminations are interpreted in terms of the decreasing orders of bond energy E(C-C) > E(C-Si) > E(C-Ge) > E(C-Sn) and E(Pd-SiH3) > E(Pd-GeH3) > E(Pd-SnH3) much greater than E(Pd-CH3). The moderate activation barriers of C-Si, C-Ge, and C-Sn reductive eliminations are reflected in their transition state structures, in which SiH3, GeH3, and SnH3 groups can interact with the allyl carbon atom, keeping the Pd-SiH3, Pd-GeH3, and Pd-SnH3 bonds intact. These features result from the hypervalency of these elements. In the C-C reductive elimination, the Pd-CH3 bond considerably weakens but the allyl-CH3 bond is not completely formed at the TS, which is consistent with no hypervalency of the C atom. The eta(1)-allyl form, Pd(XH3)(eta(1)-C3H5)(PH3), is much less stable than R-X by 7-8 kcal/mol. Intrinsic reaction coordinate calculations clearly show that the C-C reductive elimination occurs not through the eta(1)-allyl form but directly from Pd(CH3)(eta(3)-C3H5)(PH3) if PH3 does not exist in excess. If excess PH3 exists in the reaction medium, the C-X reductive elimination via Pd(XH3)(eta(1)-C3H5)(PH3)(2) is not excluded. The (eta(3)-C3H5)-XH3 (X = C, Sn) reductive elimination requires a larger activation energy than the CH3-XH3 reductive elimination, because the Pd-(eta(3)-C3H5) bond is stronger than the Pd-CH3 bond.