Recent research has increasingly focused on more sustainable methods for epoxide production, particularly through the use of vegetable oils. Palm stearin, a byproduct of palm oil refining, was selected for this study due to its abundance, low cost, and favorable chemical properties for epoxidation. This study explores the mechanism of epoxidation of palm stearin using in situ peracids, with sulfuric acid as the catalyst. The Taguchi method was applied to determine the optimal levels of various process parameters involved in the epoxidation. The results identified the most favorable conditions for each parameter: (A) reaction temperature at 65 °C (level 1), (B) stirrer speed at 100 rpm (level 3), and (C) catalyst loading at 0.4 g (level 3). Under these optimal conditions, a relative oxirane conversion (RCO) of 31.79% was obtained. To further analyze the process, a mathematical model was developed using the 4th-order Runge–Kutta method. The simulation results demonstrated a high level of agreement with the experimental data, with a coefficient of determination (R2) of 0.992, confirming the model’s accuracy and strong predictive capability.