With use of the pseudopotential local-density-functional approach, the lattice constant, the x parameter for atomic coordinates, and the phonon frequency of the mode Γ+1 are calculated for the Si-III (BC-8) crystal phases of Si and Ci. The results agree well with available experimental data for the BC-8 phases of Si. From the total-energy curves of the diamond and the BC-8 phases of Si, we find that the BC-8 phase of Si is not stable at ambient pressure or at high pressure. The diamond—BC-8 (I-III) transition of Si will not occur quasistatically. Comparing the diamond, the BC-8, and the simple-cubic phases of C, we find that diamond will first transform to the BC-8 phase at 12 Mbar and then to the simple-cubic phase at 27 Mbar under quasistatic conditions.