A numerical study of solidification of faceted 1 2 3 (YBa2CU3O7-x) crystals from liquid +2 1 1(Y2BaCuO5) phases was performed and compared with experimental results to clarify the formation mechanism of solidification structure. The effects of growth mode and conditions on the microstructures of 1 2 3 crystals were studied by two-dimensional numerical simulation of peritectic growth of faceted cellular 1 2 3 crystal during unidirectional solidification of YBCO. The basic peritectic growth model consisted of: (a) growth of faceted 1 2 3 crystal, (b) melting of 2 1 1 particles in the liquid, and (c) solute diffusion in the liquid. The growth rate (Ii) of faceted 1 2 3 crystal is approximated by: R = a(g)(.)DeltaT(k)(2), where ag is a kinetic growth constant, and DeltaT(k) is the kinetic undercooling on the faceted interface. The melting rate (R-m) of 2 1 1-particles in the liquid was given by the above equation with kinetic melting constant (a(m)) and superheating (DeltaT(m)). Solute distributions in the liquid in front of the 1 2 3 growth interface were calculated by FDM. The distributions of residual 2 1 1 particles and liquid pools in the 1 2 3 were calculated from the experimentally obtained log-normal distributions of 2 1 1 particles in the liquid, and the calculated results agreed well with the experimental ones.