We report the growth of single crystals by a flux method in ambient pressure and tri-axial orientation under modulated rotation magnetic fields (MRFs) on REBa 2 Cu 4 O 8 (RE124, RE; rare earth elements) compounds. RE124 crystals were grown for RE = Y, Sm, Eu, Gd, Dy, Ho, Er, Tm, and Yb through appropriate choice of source compounds. All the obtained RE124 powders were tri-axially aligned in MRF of 10T, whereas magnetization axes depended on the type of RE. Moreover, it was found from the changes in the degrees of c-axis and inplane orientation that triaxial magnetic anisotropies of RE124 also depended on the type of RE. This indicates that it appropriate choice of RE is important for the fabrication of tri-axial oriented ceramics in lower magnetic field conditions.