Transition structures for both uncatalyzed and BF3-catalyzed Diels-Alder reactions involving furan and methyl vinyl ketone have been determined at the hybrid DFT (B3LYP/6-31G*) level of theory. The transition structures are predicted to be relatively concerted and highly asynchronous in all cases. A subsequent bond-order analysis has been carried out at the MP2/6-31G*//B3LYP/6-31G*. The role of the Lewis acid and the origin of the endo selectivity have been discussed in terms of the nature and number of interactions present in the four possible transition structures. The partition of the potential energy barrier has also been used to estimate the contributions of the pure deformation energy and the differential interaction between the reaction partners on passing from the ground state to the saddle point. This analysis reveals that the major influence arises from the heterodiene-dienophile interaction instead of that corresponding to a BF3-dienophile interaction.