The growth patterns of cellulars in directional solidification are investigated numerically using the cellular automata (CA) model in two dimensions. A criterion which determine whether the cellulars reach stable state is derived from the analysis of simulated results. The simulated results also show that it is easy for tip splitting to appear for cellulars when the surface tention anisotropy is very small. So it is hard to obtain stable cellular arrays. However, if the amplitude of surface tention anisotropy is strong enough, it is easy to obtain stable cellular arrays. And the intensity of surface energy anisotropy can considerably influence the stable cellular patterns. The stronger the surface energy anisotropy, the smaller the stable cellular spacing and the cellular tip radius are, and the smaller the ratio between tip radius and cellular spacing, the smaller the tip concentration and the tip undercooling are.