Detailed simulations are reported for the dynamics of electrons and nuclei during the cis to trans photoisomerization of stilbene. Our method, which employs a semiclassical description of both the nuclear motion and the radiation field, is described in the text. After excitation of electrons from the HOMO to the LUMO by a femtosecond-scale laser pulse, two principal avoided crossings are observed between the HOMO and LUMO levels, each of which leads to substantial depopulation of the LUMO. Based on our results and those of other groups, we propose that the first such HOMO-LUMO coupling can lead to the formation of 4a,4b-dihydrophenanthrene (DHP). The second coupling, on the other hand, leads to the formation of trans-stilbene. It is found that pyramidalization of the two carbon atoms of the vinyl group is involved significantly in both couplings, and that rotation of the two phenyl rings, together with their interaction, plays an important role in the first coupling. The occurrence along the same trajectory of two couplings, one leading to DHP and the other leading to isomerization, is a significant observation, and one which indicates that further theoretical and experimental investigations would be of considerable interest.