Conventional fusion joining methods, such as resistance spot welding (RSW), have been demonstrated to be ineffective for magnesium alloys. However, self-pierce riveting (SPR) has recently been shown as an attractive joining technique for lightweight metals, including magnesium alloys. While the SPR joining process has been experimentally established on magnesium alloys through trial and error, this joining process is not fully developed. As such, in this work, we explore simulation techniques for modeling the SPR process that could be used to optimize this joining method for magnesium alloys. Due to the process conditions needed to rivet the magnesium sheets, high strain rates and adiabatic heat generation are developed that require a robust material model. Thus, we employ an internal state variable (ISV) plasticity material model that captures strain-rate and temperature dependent deformation. In addition, we explore various damage modeling techniques needed to capture the piercing process observed in the joining of magnesium alloys. The simulations were performed using a two-dimensional axisymmetric model with various element deletion criterions resulting in good agreement with experimental data. The simulations results of this study show that the ISV material model is ideally suited for capturing the complex physics of the plasticity and damage observed in the SPR of magnesium alloys.