Sodium-sulfur (NaS) batteries are a promising energy storage technology that features high energy density, high cycle life, and no self-discharge. One of the cell design considerations that can affect the performance and construction of NaS batteries is cell geometry. While the planar geometry has advantages in power output, cell packing, ease of assembly, and thermal management, it has thermo-mechanical issues in sealing, which makes it less commercialized than the tubular geometry. In this work, the first multiphysics model of a NaS cell with a planar geometry was developed by extending an existing multiphysics model for a NaS cell with a tubular geometry. A previously developed multiphysics model for the tubular NaS cell was first adapted into COMSOL Multiphysics®. The model’s results were then validated against experimental discharge profiles and surface temperatures. After this, a planar NaS cell was simulated using the dimensions of an experimental planar cell, with the mass, heat, and charge transfer equations and parameters previously used in the tubular multiphysics model. The results from the planar model were then validated through comparison to experimental discharge profiles for a planar cell. The developed model can be used in future research and development of NaS batteries by comparing performance parameters of the planar geometry such as discharge profiles, energy densities, and temperatures with a multiphysics model of the tubular NaS battery.