The most common type of electric propulsion in space exploration is the Hall Effect Thruster (HET), mainly due to its high specific impulse and high thrust to power ratio. However, uncertainties about the thruster's lifetime prediction have prevented widespread integration of HETs. Among these limitations, wall erosion of acceleration channel is of greatest concern. The experimental methods of erosion are time consuming and costly, and they are often limited to one single configuration. Hence, developing a computational model not only decreases the costs but also shortens the design time of a HET. This thesis investigates the feasibility of a uid erosion modelling with a multi-physics software (COMSOL) to further decrease the time and the development cost. First of all, this thesis provides an overview of available plasma modelling techniques and the physics behind the erosion phenomenon. Moreover, the effective parameters and available modules in the multiphysics software as well as their theoretical background were studied and discussed in detail. The Electron Anomalous phenomenon and pressure instability are determined as the main limiting factors for such a model. A non-magnetized model is included to find an optimal value for pressure and to reduce the probability of pressure instability occurrence in magnetized model. To fulfill this task, several simulations for various pressure values (0.005 Torr, 0.05 Torr, and 0.5 Torr) were conducted. Next, the simulation of magnetized/full model has been carried out with addition of magnetic coils in non-magnetized model. To avoid the Electron Anomalous phenomenon, the Bohm diffusion approach was implemented. In addition, a full Particle-In-Cell (PIC) simulation of a typical HET (SPT-100) with the similar input parameters as in fluid model was conducted, and the results were compared and validated using experimental data. The PIC model was intended to be utilized to investigate the accuracy of erosion model in multiphysics software. The results of this thesis indicate that current application of erosion model in COMSOL is not possible whilst high accuracy of the erosion model based on PIC approach can be achieved. Finally, the application of semi-empirical method through direct input of magnetic field data can allow short time simulation of a HET in COMSOL to gain insight about the preliminary behaviour of plasma, however, the simulation of an erosion model requires either a built-in PIC algorithm in COMSOL or a PIC based code.