The hydrogen abstraction reactions of hydrogen atom with germane and silane have been studied by using ab initio molecular orbital theory and the canonical variational transition state theory. The potential energy surface information is calculated at the UQCISD/6-311+G** level of theory. Energies along the minimum energy paths are improved by a series of single-point G2//QCISD calculations. The changes of the geometries, generalized normal-mode vibratioanal frequencies, and total curvatures along the reaction paths are discussed. The reaction thermal rate constants for the temperature range 200-1600 K are obtained by canonical variational transition state theory with small-curvature tunneling correction. The calculated results show that the variational effect is small and in the lower temperature range, the small curvature effect is important for the two reactions. Good agreement with experimental values is found for the rate constants over the measured temperature ranges. The rate constants can be fitted to the three-parameter expressions through the whole temperature range 200-1600 K: k(GeH4 + H) = 2.0 x 10(7) T-2.12 exp(-492/T) cm(3) mol(-1) s(-1); k(SiH4 + H) = 2.27 x 10(5) T-2.69 exp(-779/T) cm(3) mol(-1) s(-1).