Some computational results on directional solidification of a binary alloy obtained by using the phase field model are reported. Frozen temperature approximatio n is adopted to simplify the modeling. The onset of morphological instability, t he pattern evolution and the solute redistribution are shown. The cell to planar interface transition is modeled near the high velocity absolute stability condi tion. The cell spacings, tip temperatures and solute partitioning coefficients a t different velocities are calculated. The solute trapping is also observed.