It is generally assumed that element synthesis will take place readily under the extreme conditions believed to exist in supernova explosions. We have examined the types of thermonuclear reactions that can occur in a supernova shock wave which propagates through the stellar envelope, in which a temperature ~5 × 109 °K may occur for ~10−2 seconds. The calculations are performed using a network of nuclei connected to their neighbors by absorption or emission of neutrons, protons, alpha particles and photons (Truran et al. 1966). The results show that iron-peak elements can be produced by a supernova shock wave, but the iron-peak composition observed in nature is not produced unless some transformation of protons to neutrons has taken place in the material before the passage of the shock wave. Furthermore, a neutron flux sufficient to drive the rapid neutron-capture process is not attained under these conditions in the stellar envelope.