A two-dimensional, time-dependent model and code have been developed to model electrothermal (ET) plasma discharges. ET plasma discharges are capillary discharges that draw tens of kA of electric current. The current heats the plasma, and the plasma radiates energy to the capillary walls. The capillary walls ablate by melting and vaporizing and by sublimation. The newly developed model and code is called the Three-fluid, 2D Electrothermal Plasma Flow Simulator (THOR). THOR simulates the electron, ion, and neutral species as separate fluids coupled through interaction terms. The two-dimensional modeling capabilities made available in this new code represent a tool for the exploration and analysis of the physics involved in ET plasma discharges that has never before been available. Previous simulation models of ET plasma discharges have relied primarily on a 1D description of the plasma. These models have often had to include a tunable correction factor to account for the vapor shield layer - a layer of cold ablated vapor separating the plasma core from the ablating surface and limiting the radiation heat flux to the capillary wall. Some studies have incorporated a 2D description of the plasma boundary layer and shown that the effects of a vapor shield layer can be modeled using this 2D description. However, these 2D modeling abilities have not been extended to the simulation of pulsed ET plasma discharges. The development of a fully-2D and time-dependent simulation model of an entire ET plasma source has enabled the investigation of the 2D development of the vapor shield layer and direct comparison with experiments. In addition, this model has provided novel insight into the inherently 2D nature of the internal flow characteristics involved within the plasma channel in an ET plasma discharge. The model is also able to capture the effects of inter-species interactions. This work focuses on the development of the THOR model. The model has been implemented using C++ and takes advantage of modern supercomputing resources. The THOR model couples the 2D hydrodynamics and the interactions of the plasma species through joule heating, ionization, recombination, and elastic collisions. The analysis of simulation results focuses on emergent internal flow characteristics, direct simulation of the vapor shield layer, and the investigation of source geometry effects on simulated plasma parameters. The effect of elastic collisions between electrons and heavy species are shown to affect internal flow characteristics and cause the development of back-flow inside the ET plasma source. The development of the vapor shield layer has been captured using the diffusion approximation for radiation heat transfer within the ET plasma source with simulated results matching experimental measurements. The relationship between source radius and peak current density inside ET plasma discharges has also been explored, and the transition away from the ablation-controlled operation of ET plasma discharges has been observed.Ph. D.