Recent X-ray diffraction experiments (M. Hanfland, U. Schwarz, K. Syassen, K. Takemura, Phys. Rev. Lett., 82 (1999) 1197) show that the intermediate high-pressure phase of Si-VI is isostructural with Cs-V. The structure is base-centered orthorhombic, space group Cmca, with 8 atoms in the primitive cell (16 in the orthorhombic unit cell, oC16). We present here ab initio calculations that include relaxations of Si in the primitive hexagonal (ph), the orthorhombic (Cmca) as well as the hexagonal close packed (hcp) structure. The force calculations confirm the atomic positions obtained by analyses of the experimental data, the calculated P-V relations for the three phases are very close to the observed isotherms, and the calculated ph --> oC16 --> hcp transition pressures, 33 +/- 2 and 41 +/- 5 GPa, agree well with experiments. A comparative calculation for Cs-V is briefly discussed. (C) 1999 Elsevier Science Ltd. All rights reserved.