This study focuses on the behavior of volatile organic compounds in beef after irradiation with 1 MeV accelerated electrons with doses ranging from 0.25 kGy to 5 kGy to find reliable dose-dependent markers that could be used for establishing an effective dose range for beef irradiation. GC/MS analysis revealed that immediately after irradiation, the chemical yield and accumulation rate of lipid oxidation-derived aldehydes was higher than that of protein oxidation-derived aldehydes. The nonlinear dose-dependent relationship of the concentration of volatile organic compounds was explained using a mathematical model based on the simultaneous occurrence of two competing processes: decomposition of volatile compounds due to direct and indirect action of accelerated electrons, and accumulation of volatile compounds due to decomposition of other compounds and biomacromolecules. A four-day monitoring of the beef samples stored at 4 °C showed that lipid oxidation-derived aldehydes, protein oxidation-derived aldehydes and alkanes as well as alcohol ethanol as an indicator of bacterial activity were dose-dependent markers of biochemical processes occurring in the irradiated beef samples during storage: oxidative processes during direct and indirect action of irradiation, oxidation due to the action of reactive oxygen species, which are always present in the product during storage, and microbial-enzymatic processes. According to the mathematical model of the change in the concentrations of lipid oxidation-derived aldehydes over time in the beef samples irradiated with different doses, it was found that doses ranging from 0.25 kGy to 1 kGy proved to be most effective for beef irradiation with accelerated electrons, since this dose range decreases the bacterial content without considerable irreversible changes in chemical composition of chilled beef during storage.