Density functional B3LYP/6-31G(d) and ab initio G3(MP2,CC) calculations have been carried out to determine thermal rate constants of direct H abstraction reactions from four- and five-ring polycyclic aromatic hydrocarbons (PAH) chrysene and benzo[a]pyrene by various radicals abundant in combustion flames, such as H, CH3, C3H3, and OH, using transition state theory. The results show that the H abstraction reactions with OH have the lowest barriers of ∼4 kcal mol-1, followed by those with H and CH3 with barriers of 16-17 kcal mol-1, and then with propargyl radicals with barriers of 24-26 kcal mol-1. Thus, the OH radical is predicted to be the fastest H abstractor from PAH. Even at 2500 K, the rate constant for H abstraction by H is still 34% lower than the rate constant for H abstraction by OH. The reaction with H is calculated to have rate constants 35-19 times higher than those for the reaction with CH3 due to a more favorable entropic factor. The reactions of H abstraction by C3H3 are predicted to be orders of magnitude slower than the other reactions considered and their equilibrium is strongly shifted toward the reactants, making propargyl an inefficient H abstractor from the aromatics. The calculations showed strong similarity of the reaction energetics in different H abstraction positions of benzo[a]pyrene and chrysene within armchair and zigzag edges in these molecules, but clear distinction between the armchair and zigzag sites. The zigzag sites appear to be more reactive, with H abstraction rate constants by H, CH3, and OH being respectively 37-42%, a factor of 2.1, and factors of 8-9 higher than the corresponding rate constants for the H abstraction reactions from armchair sites. Although the barrier heights for the two types of edges are similar, the entropic factor makes zigzag sites more favorable for H abstraction. Rate expressions have been generated for all studied reactions with the goal to rectify current combustion kinetics mechanisms.