Phased array radar systems have a wide variety of applications in engineering and physics research. Phased array design usually requires numerical modeling with expensive commercial computational packages. Using the open-source MIT Electrogmagnetic Equation Propagation (MEEP) package, a set of phased array designs is presented. Specifically, one and two-dimensional arrays of Yagi-Uda and horn antennas were modeled in the bandwidth [0.1–5] GHz, and compared to theoretical expectations in the far-field. Precise matches between MEEP simulation and radiation pattern predictions at different frequencies and beam angles are demonstrated. Given that the computations match the theory, the effect of embedding a phased array within a medium of varying index of refraction is then computed. Understanding the effect of varying index on phased arrays is critical for proposed ultra-high energy neutrino observatories which rely on phased array detectors embedded in natural ice. Future work will develop the phased array concepts with parallel MEEP, in order to increase the detail, complexity, and speed of the computations.