The 1,3-dipolar cycloaddition reaction is a powerful tool for the cycloaddition of nitrile oxides to olefins, and this reaction is of considerable interest to obtain isoxazolines. Density functional theory (DFT) was used to study the 1,3-dipolar cycloaddition reaction mechanism that initially occurs between benzonitrile oxide and vinylacetic acid to yield a bicyclo, from successive cycloadditions. PBE1PBE, B3LYP and CAM-B3LYP functionals were used together with 6-311+G(2d,p) basis set. CCSD(T)/6-311+G(2d,p) calculations were done to compare the DFT energy barriers. The solvent effects were included using polarizable continuum model (PCM), with three different solvents. In the first cycloaddition, only the 3,5-regioisomer is expected. In the gas phase, the β face attack, that originates the trans-bicyclo, is slightly favored, but the cis-bicyclo is considerably more stable. However, the α face attack was favored with solvent effects. The PBE1PBE functional gives the closest activation energies and reaction energies to CCSD(T). The inclusion of solvent effects changes the preferential rotamer in each cycloaddition.