This paper describes the first detailed computational mechanistic study of the Julia-Kocieński olefination between acetaldehyde (1) and ethyl 1-phenyl-1H-tetrazol-5-yl sulfone (2), considered a paradigmatic example of the reaction between unsubstituted alkyl PT sulfones and linear aliphatic aldehydes. The theoretical study was performed within the density functional approach through calculations at the B3LYP/6-311+G(d,p) level for all atoms except sulfur for which the 6-311+G(2df,p) basis set was used. All the different intermediates and transition states encountered along the reaction pathways leading to final E and Z olefins have been located and the relative energies calculated, both for the reactions with potassium- and lithium-metalated sulfones, in THF and toluene, respectively. We have essentially confirmed the complex multistep mechanistic manifold proposed by others; however, the formation of a spirocyclic intermediate in the Smiles rearrangement was excluded. Instead, we found that this step involves a concerted, though asynchronous, mechanism. Moreover, our calculations nicely fit with the diastereoselectivities observed experimentally for potassium- and lithium-metalated sulfones, in THF and toluene, respectively.