An investigation was made of whether the cosmic abundances of the elements in the iron peak can be explained in terms of the rapid nuclear process supposed to take place during the initial phases of supernova explosions. From calculations of rates reaction induced by protons, alpha particles, and their antiparticles, it is seen that the formation of elements, beginning with Ca/sup 40/, is determined by (p, gamma ) and ( gamma ,p) reactions and beta /sup +/+- decays which are faster than the characteristic time scale of nuclear synthesis duration in the exploding envelope of a supernova, 10/sup 2/ to 10/sup 3/ sec. The abundances of nuclei were calculated assuming that a steady state is reached in which the abundance of each nuclide is proportional to its proton-capturing or beta /sup +/ decay time. The final abundances of stable isotopes were determined by considering only beta /sup +/ decays as the freezing reaction in the envelope cooling stage. Considering the uncertainity of nuclear masses of proton-rich nuclides, it is concluded that the abundances of the iron peak elements can be explained in terms of the rapid process. (B.O.G.)