Accurate description of reactions between propyl radicals and molecular oxygen is an essential prerequisite for modeling of low-temperature propane oxidation because their multiple reaction pathways either accelerate the oxidation process via chain branching or inhibit it by forming relatively stable products. The CBS-QB3 level of theory was used to construct potential energy surfaces for n-C3H7 + O-2 and i-C3H7 + O-2. High-pressure rate constants were calculated using transition state theory with corrections for tunneling and hindered rotations. These results were used to derive pressure- and temperature-dependent rate constants for the various channels of these reactions under the framework of the Quantum Rice-Ramsperger-Kassel (QRRK) and the modified strong collision (MSC) theories. This procedure resulted in a thermodynamically consistent C3H7 + O-2 submechanism, which was either used directly or as part of a larger extended detailed kinetic mechanism to predict the loss of propyl and the product yields of propylene and HO2 over a wide range of temperatures, pressures, and residence times. The overall good agreement between predicted and experimental data suggests that this reaction subset is reliable and should be able to properly account for the reactions of propyl radicals with O-2 in propane oxidation. It is also demonstrated that for most conditions of practical interest only a small subset of reactions (e.g., isomerization, concerted elimination of HO2, and stabilization) controls the oxidation kinetics, which makes it possible to considerably simplify the mechanism. Moreover, we observed strong similarities in the rate coefficients within each reaction class, suggesting the potential for development of relatively simple rate constant estimation rules that could be applied to analogous reactions involving hydrocarbon radicals that are too large to allow accurate detailed electronic structure calculations.