Conventional fusion joining methods such as resistance spot welding have been demonstrated to not be effective for magnesium alloys. Therefore, self-pierce riveting (SPR) has been presented as an attractive joining technique for these lightweight metals. However, SPR must be performed at elevated temperatures because of the low ductility of magnesium alloys at room temperature. Even though the SPR joining process has been established on magnesium alloys, this joining process is not optimized. As such, this study establishes the first attempt at simulating the SPR of magnesium alloys through the use of the finite element method. An internal state variable (ISV) plasticity and damage material model was employed with results in good agreement to experimental data. The results of this study show that the ISV material model is ideally suited for modeling the SPR process in magnesium alloys.