Abstract The 1,3-dipolar cycloaddition of the Benzyl azide and its derivatives( -H, 2-CI, 3-CI, 3-OCH3, 4-OCH3, 4-NO2, 2,6-Cl ) with Cinnamic acid was studied theoretically using Density Functional Theory (DFT) MO62X with the basic set 6-31g(d) with solvents: water, dimethyl sulfoxide(DMSO), Acetonitrile, Ethanol, Tetrahydrofuran (THF), Dimethyl Ether and Heptane. We have identified thermodynamic properties and kinetic factors using Polarization Continuous Method PCM in the level of theory M062X/6-31 g (d). The results of the level of theory M062X/6-31g (d) indicate that the one, 3-dipolar cycloaddition of the Benzyl azide carried out spontaneously in the gas state to form several stable energy products. P1 and P2 are most stable, but all the reactions are very slow and one of the products P1 is more spontaneous than P2 but the formation reaction of P2 is faster. On the other hand, it is found that solvents to have no actual effects on the rates of these reactions but it was observed that TS-P1 transition state energy for all substitutes was lower than TS-P2 transition state energy.