The abstraction and exchange reactions of hydrogen atom with methane and silane have been studied at high levels of ab initio molecular orbital theory. Very large basis sets were employed in this study. Geometries were optimized at the MP-2 level with at least TZ+2P+f basis sets. Even larger basis sets were used for the final energy calculations at the QCISD(T) level. The calculated reaction energies (Delta H(298)) for abstraction are 0.42 and -12.2 kcal/mol for C and Si, respectively, in excellent agreement with the experimental results. The classical barrier heights for abstraction are 15.06 and 5.39 kcal/mol for C and Si, respectively. Inclusion of zero-point effects lowers the barriers to 13.63 and 4.59 kcal/mol for the C and Si reactions, respectively. The exchange process in the carbon system occurs with inversion of configuration with a classical barrier height of 38.10 kcal/mol. The exchange process for the silicon system occurs with classical barrier heights of 12.93 and 13.46 kcal/mol for the inversion and retention of configuration processes, respectively. Transition-state theory was used to calculate rate constants for the abstraction reactions. Comparison with the experimental values suggests that the calculated classical barrier heights could be too high by 0.5-2 kcal/mol for the abstraction reactions.