The structure of the Ba5R8Zn4O21 series (R=lanthanides) was investigated using X-ray Rietveld refinements. The compounds were successfully prepared for R=Eu, Gd, Dy, Ho, Er, Tm, and Yb. Ba5R8Zn4O21 crystallizes in the tetragonal space group I4/m; for R=Yb to Eu, a ranges from 13.635 02(5) to 13.960 62(9) Å, c from 5.658 46(3) to 5.784 83(5) Å, and V from 1051.987(8) to 1127.459(14) Å3. The Zn2+ ions adopt a fivefold distorted square pyramidal coordination. The seven-coordinate R3+ reside in monocapped trigonal prisms. These prisms share edges, and form layers stacked along the c axis. There are two types of BaO polyhedra: bicapped square prisms (BaO10), and irregular BaO10 polyhedra. For larger R, Ba5R8Zn4O21 was not stable, and tetragonal BaR2ZnO5(La, Nd) and orthorhombic BaR2ZnO5(Sm) phases were observed instead.