Abstract: For purposes relating to force protection through advancments in multiscale materials modeling, this report explores the use of the phase-field method for simulating microstructure solidification of metallic alloys. Specifically, its utility was examined with respect to a series of increasingly complex solidification problems, ranging from one dimensional, isothermal solidification of pure metals to two-dimensional, directional solidification of non-isothermal, binary alloys. Parametric studies involving variations in thermal gradient, pulling velocity, and anisotropy were also considered, and used to assess the conditions for which dendritic and/or columnar microstructures may be generated. In preparation, a systematic derivation of the relevant governing equations is provided along with the prescribed method of solution.