In this work, we have carried out a quantum chemistry and computational kinetics study on the reactivity of six natural polyphenolic compounds found in soy and soybean products, towards two peroxyl free radicals (˙OOH and ˙OOCH3), in aqueous and lipid simulated biological environments. We have considered two reaction mechanisms: hydrogen transfer (HT) and single electron transfer (SET). Rate constants and relative branching ratios for the different paths contributing to the overall reaction, at 298.15 K, are reported. In water media, equol (EQL) reacts faster with ˙OOH radicals, followed by 8-hydroxiglycitein (8-HGLY) and genistein (GEN). Regarding the reactivity towards ˙OOCH3 radicals, we found that 8-HGLY is more effective than EQL. The total HT rate constants are smaller than the SET ones for all the studied compounds. In water, the presence of the 4-piranone ring decreases the reactivity but increases the acidity which favours deprotonation, which in turn increases the capability of oxidizing via electron loss. In lipid environment, due to the unfeasibility of deprotonation, the studied polyphenols are poor antioxidants. The results were compared against similar polyphenolic antioxidants such as resveratrol previously reported in the literature.