A computational study on ground and excited states of dimethyl sulfoxide (DMSO) and the hypothetical molecule H2SO is reported. Full valence CASSCF/6-311+G(3df,2p) with a multireference perturbation theory correction was used for the latter, while DMSO was examined with an active space that neglected only the CH bonds and an analogous basis set that neglected polarization functions on H. A realistic value of 41.5 kcal/mol was obtained for the ground state pyramidal inversion of sulfur for DMSO, though no directly comparable experimental value is available. Calculations were also carried out on singlet and triplet excited state surfaces of both A' and A " symmetry. Relaxed excited state geometries fairly near the ground state geometry were found, but perhaps more importantly, excited state stationary points were also found in C-2 nu symmetry. These were the lowest energy of any geometry on their respective surfaces. This leads to the speculation that photochemical stereomutation of alkyl sulfoxides may occur without C-S bond cleavage in a mechanism formally analogous to the photochemical cis-trans isomerization of olefins.