We have studied the Diels-Alder reaction of 1,3-butadiene with all nonequivalent bonds of Y3N@D-3h-C-78 at the BP86/TZP//BP86/DZP level of theory. The results obtained are compared with those extracted from a previous study on the free and SC3N-endohedral C-78 fullerene (J. Am. Chem. Soc. 2008, 130, 6206-6214). Our study shows that the most stable regioisomer for the Y3N compound is obtained for the reaction over a corannulene-type [5,6] bond (d), which exhibits the longest bond distance (1.47 angstrom) and a large pyramidalization angle. As far as we know, this is the first case of a cycloaddition reaction where the most stable addition is obtained over one of the longest C-C bonds in the cage. In contrast to SC3N@D-3h-C-78, where bonds close to the scandium atoms were destabilized, this bond d has one of the yttrium atoms in close contact. This preference for reacting with those bonds situated close to the yttrium atoms is due to two different factors: first, the D-3h cage is extremely deformed, especially in the areas situated close to the yttrium atoms (which contain the most reactive bond d), so the attack reduces the strain energy of the cage; second, in the final adduct, the Y3N cluster gets additional space to adopt a more planar configuration. Since it has been shown (J. Phys. Chem. B 2007, 111, 3363-3369) that the D-3h isomer is not the most favorable isomer for endohedral Y3N@C-78 (at variance with SC3N@C-78), we also studied the more favorable C-2 somer. The latter contains [5,5] bonds, which are shown to be the most reactive bonds for cycloaddition, in contrast to previous theoretical predictions (J. Org. Chem. 2006, 71, 46-54). This preference for [5,5] bonds is observed for the C-2 isomers of both endohedral (SC3N, Y3N) and free C78 fullerene and is dictated by the fullerene strain energy. We therefore expect that the Diels-Alder reaction on other endohedral metallofullerenes that have already been synthesized (e.g., Tm3N@C-2-C-78, DY3N@C-2-C-78) might lead to the same [5,5] adduct.