The Diels - Alder reactions of furan and some derivatives with maleic anhydride have been studied using methods of density functional theory (DFT): B3LYP, B3PW91, MPW1PW91 and MPW1BPE with 6-31g(d) bases set and proceeding energy cor-relation at MP4 level of theory with same bases set. The results of this study showed that, for the Diels - Alder reaction of Furan and 2-methyl furan with maleic anhydride, the reaction of formation of exo-adduct proceeds under thermodynamical control, and the reaction of formation of endo-adduct proceeds under kinatic control, but for the 2-furylmethanol, 2- furylmethyl acetate and 2-furylmethyl benzoate, the reactions of formation of exo-adduct proceed under thermodynamical and kinetic controls. The MPW1BPE/6-31g(d) level of theory was advanced susceptible results by comparison with the reference experimental data; exactly for furan-maleic anhydride Diels - Alder reaction.