Trans-p-coumaric and trans-sinapinic acids are cinnamic acid`s derivatives which show strong antioxidant properties. In this work full optimization of both chemical structures and their radical, cation radical and anionic forms in vacuum and water medium has been performed, and antioxidant descriptors: Bond Dissociation Enthalpy, Adiabatic Ionization Potential, Proton Dissociation Enthalpy, Proton Affinity, Electron Transfer Enthalpy, Gas Phase Acidity, Free Gibbs Energy have been calculated. The Highest Occupied and Lowest Unoccupied Molecular Orbital energies have been employed to determine groups in compounds studied with the highest electron density. All calculations were performed using Gaussian 03W software package at the DFT level of theory (B3LYP hybrid functional) together with 6-311+G(2d,2p) basis set. Strong antioxidant properties of both investigated compounds were determined in this study. Based on the results it may be suggested that trans-p-coumaric and transsinapinic acids react according to the Hydrogen Atom Transfer mechanism in vacuum and according to Single- Electron Transfer followed by the Proton Transfer mechanism in water medium. Moreover, in both compounds studied the O-H bond is a preferred place of free radical attack.