Studies of the kinetics of electrophoretic deposition (EPD) processes have generally focused on electrode geometries that yield analytical solutions, such as infinite parallel planes and concentric cylinders. In this article, we construct a finite element model for EPD of material onto a planar strip electrode, which shows excellent qualitative agreement to experimental results in a similar system. Notably, we demonstrate that the presence of the edges of the electrode lead to a singularity in the electric field that significantly affects the morphology of the deposit at short times or for thin deposits.