Structural phase transitions of germanium at pressures up to 190 GPa have been investigated by means of angle-dispersive x-ray powder diffraction using synchrotron radiation. Near 100 GPa the primitive hexagonal modification of Ge transforms to an orthorhombic phase with 16 atoms per unit cell. The results of full-profile Rietveld refinements in space group $\mathrm{Cmca}$ indicate that the orthorhombic modification of Ge is isotypic to the phase Si-VI. Near 160--180 GPa Ge undergoes a transition to a structure assigned as hexagonal close packed (hcp). Ab initio calculations of pressure-dependent enthalpies and optimized structural parameters are presented for different structures of Ge. The calculated results clearly support the observed occurrence of the $\mathrm{Cmca}$ structure in Ge.