Phenolic acids constitute a family of natural compounds that can be found in a wide variety of plants and food. Among them only ferulic, p-coumaric, chlorogenic, and caffeic acids were recently investigated. There are no data about antioxidant activity of single molecules of fertaric, coutaric, caftaric, dactylifric, and neochlorogenic acids and prenyl caffeate. In a continuation of our attempts to clarify their antioxidant activity, we present herein in silico studies concerning four mechanisms of interaction of phenolic antioxidants with free radicals: hydrogen atom transfer (HAT), (sequential proton loss electron transfer (SPLET), single electron transfer followed by proton transfer, and transition metals chelation, determining several parameters such as bond dissociation enthalpy; proton affinity; adiabatic ionization potential; highest occupied molecular orbital, lowest unoccupied molecular orbital, singly occupied molecular orbital; spin density; stabilization energy (ΔE_ISO); deprotonation enthalpy/energy (ΔH_acidity and ΔG_acidity); and second-order perturbation energy E(2). We have proved that for all studied compounds the HAT mechanism was preferred in vacuum as well as in benzene and amyl acetate solvent media, whereas SPLET approach was significantly exposed especially in water. The most active antioxidants (according to the HAT approach) were compounds prenyl caffeate, methyl caffeate, and caffeic acid phenethyl ester, whereas the activity of trans and cis isomers of chicoric derivatives was related to the SPLET protocol. We also observed that trans isomers of caffeic, ferulic, and p-coumaric derivatives were not enough effective in all environments, when compared with other studied molecules. Moreover, we have noticed that the ortho position of the phenylic ring influenced profitably on antioxidant activity in all analyzed compounds.