A practical procedure of calculating quantum rate constants for polyatomic reactions presented previously has been extended in this paper to investigate the kinetic isotope effects (KIEs) for the following reactions: D + CH4, D + C2H6, D + C2D6, and D + CH3OH. The method involves treating the quantum dynamics explicitly for bonds being broken and formed with a potential energy surface obtained from ab initio calculations (MP2 for geometry optimizations and vibrational frequencies, CCSD(T) for points on reduced dimensionality surface). Rate constants are evaluated, and we find the existence of inverse and normal kinetic isotope effects among the listed reactions. Comparison with the available experimental measurements for the D + CH4 and D + CH3OH reactions confirms the inverse KIE found in the present calculations.