The concerted and the stepwise mechanisms of the Diels-Alder reaction between butadiene and ethylene were studied by ab initio MO methods. For the stepwise mechanism, three process are included: the first process is the formation of biradical intermediate with a transition state, the second is the rotation for the: new bond axis with a transition state, and the third is the other bond formation without an energy barrier. The transition state for the first process has a higher energy barrier of 4 kcal/mol than that for the second process at the CAS-MP2/6-311+G(d,p) calculation level. For the concerted mechanism, the energy barrier height of the transition state is 2.7 kcal/mol lower than that of the first process of the stepwise mechanism by the CAS-MP2/6-311+G(d,p) level. Both reaction mechanisms were analyzed by a CiLC-IRC method. The CiLC-IRC analysis shows the nature of the aromaticity for the transition state of the concerted mechanism. The CiLC-IRC analysis also shows that the transition state of the second process of the stepwise mechanism causes from the static energy as the rotational barrier of methyl group.