The depletion of bauxite reserves has prompted the research of various types of soil as alternative sources of aluminum, such as the peat clay used in this study. The complexity of the minerals requires a more efficient leaching methods, while microwave-based leaching offers a potential approach through rapid and uniform heating. This study examines the effect of microwave power, HCl concentration, operating temperature, and particle size on the leaching efficiency of aluminum from peat clay soil. The leaching process was modeled using two approaches, namely the shrinking core (SC) model and the broken-intact cell (BIC) model under pseudo-steady state conditions. The results showed that increasing HCl concentration, microwave power, and temperature accelerated leaching, while increasing particle size decreased leaching efficiency. Optimum conditions were achieved at 4 M HCl concentration, 100 W power, 40 °C temperature, and 0.0074 cm particle size. The shrinking core (SC) model showed better fit under most conditions, while the intact-broken cell (BIC) model was more accurate at lower temperatures and particle sizes. The simulation results showed that the most suitable parameter values in the SC model were De = 0.0049 cm2/s, k = 10.5 cm/s, and kc = 2.49 cm/s, while in the BIC model De = 0.04808 cm2/s and K = 0.02689 g/cm3 were obtained. These results confirm the superiority of the SC model in representing microwave-based leaching mechanisms in general, while the BIC model provides additional insights under diffusion-limited conditions. Process Performance Index (PPI) analysis showed that optimum conditions were achieved at 4 M HCl and 40 °C, but lower acid concentrations also yielded competitive PPI. This confirms that leaching effectiveness is determined by a combination of alumina recovery and reagent consumption efficiency. These findings contribute to the development of leaching kinetics models and the optimization of more efficient and energy-saving aluminum extraction processes.