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 REBa2Cu4O8 (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 tri-axial 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.