Oxidative stress makes it difficult to preserve food and negatively affect the applicability of polymeric packaging. It is typically caused by an excess of free radicals, and it is dangerous to human health, resulting in the onset and development of diseases. The antioxidant ability and activity of ethylenediaminetetraacetic acid (EDTA) and Irganox (Irg) as synthetic antioxidant additives were studied. Three different antioxidant mechanisms were considered and compared by calculating bond dissociation enthalpy (BDE), ionization potential (IP), proton dissociation enthalpy (PDE), proton affinity (PA), and electron transfer enthalpy (ETE) values. Two density functional theory (DFT) methods were used, M05-2X and M06-2X with the 6–311++G(2d,2p) basis set in gas phase. Both additives can be used to protect pre-processed food products and polymeric packaging from oxidative stress related material deterioration. By comparing the two studied compounds, it was found that EDTA has a higher antioxidant potential than Irganox. To the best of our knowledge several studies have been carried out to understand the antioxidant potential of various natural and synthetic species, but EDTA and Irganox were not compared and investigated before. These additives can be used to protect pre-processed food products and polymeric packaging and prevent material deterioration caused by oxidative stress.