Ab initio (RHF/3-21G and RHF/6-31G* basis sets) and semiempirical (AM1 and PM3) quantum chemical calculations have been applied to a study of Diels-Alder reactions of furan and cyclopentadiene as 1,3-dienes, with norbornene and 7-oxanorbornene as dienophiles, in order to model -facial selectivities and stereoselectivities of these reactions. To achieve this goal, transition states for these reactions are located and activation energies estimated. The exclusive exo -facial selectivity exhibited in these cycloadditions are readily predicted using semiempirical or ab initio ethods. To determine stereochemical outcomes following -facial attack, ab initio calculations are required. Exo,endo stereoselectivities found experimentally, are successfully predicted by using RHF/6-31G*//3-21G or higher levels of calculations. Secondary orbital interactions are postulated to be responsible for the experimental stereoselectivities.