Directional steady-state solidification processes which are the Bridgman-type method and the zone melting method from the partial molten state, in which Y₂BaCuO₅ and liquid coexist in equilibrium, were performed under several different experimental conditions. In the Bridgman method, the temperature gradient (G) and the growth rate (R) were controlled independently at the same cooling rates. The degree of alignment of YBa₂Cu₃O_y crystals increased with increasing the G/R ratio even at the same cooling rate (6K/h). Higher G/R values were preferable for obtaining highly oriented crystal structures. The minimum limit for the continuous growth of YBa₂Cu₃O_y crystals exists between the G/R values of 301 and 482°Ch/cm². The high Jc value of 1.9×10⁴A/cm² (77K, 1T), estimated from the magnetic measurement, was obtained in the sample grown under the high G/R of 482°Ch/cm². The results of the samples grown by the zone melting method indicate that the continuous growth with large faceted solid/liquid interface can be achieved in the sample grown at 1mm/h and the volume fraction of 211 phase particles drasticaly decreases from in the liquid to the 123 phase solids at the interface. The proposed solidification model in which Y solute diffusion in the liquid limits the rate of the peritectic reaction agrees well with the experimental results.