In the nature and the engineering research, directional solidification is a very important topic, the solidification condition control can tremendously influence the characteristics of a material, for example, mechanical strength, degree of hardness and so on. Therefore if we can thoroughly understand the mechanism of solidification, we will be allowed to strengthen us to hold control over the characteristics of the material its application. This is also why scientists have such big interest in this area. In this thesis we use Phase field model and the adaptive mesh refinement(AMR) to simulate directional solidification, and two main topic are discussed. The first is phase field modeling of thin-film directional solidification of a binary alloy－from 2D to 3D transition. The two-dimensional shape can gradually transform to 3D shape. Second, we discuss the problems encountered in three-dimensional directional solidification. The property of crystal, e.g. anisotropic strength, has the influence on the crystal shape and the arrangement, and we discovered that for different anisotropic strength, the arrangement of crystal can act differently. Moreover, we have extended the results made in literature, and enabled the simulation to approach the result experiments have observed.