Transcranial direct current stimulation (tDCS) continues to demonstrate success as a medical intervention for neurodegenerative diseases, psychological conditions, and traumatic brain injury recovery. One aspect of tDCS still not fully comprehended is the influence of the tDCS electric field on neural functionality. To address this issue, we present a mathematical, multiscale model that couples tDCS administration to neuron electrodynamics. We demonstrate the model’s validity and medical applicability with computational simulations using an idealized two-dimensional domain and then an MRI-derived, three-dimensional human head geometry possessing inhomogeneous and anisotropic tissue conductivities. We exemplify the capabilities of these simulations with real-world tDCS electrode configurations and treatment parameters and compare the model’s predictions to those attained from medical research studies. The model is implemented using efficient numerical strategies and solution techniques to allow the use of fine computational grids needed by the medical community.