This study investigates the dynamic interaction behavior of a rigid square foundation embedded in a layered half-space under torsional vibrations. An adaptive finite-unit method is used to create simplified models with discrete elements. Fifteen basic units, comprising linear springs, linear dampers, and concentrated polar mass inertia, are assembled according to specific principles to generate nineteen candidate models. The equivalent model theory is utilized to ascertain the physical parameters of each element. Three equivalent criteria are established accordingly between an actual soil-foundation system and a simplified soil-foundation system in terms of static responses, dynamic amplification factors, and dynamic dissipated energy factors. An optimization analysis using a sequential search method has been conducted to determine the optimal model for accurately simulating the dynamic torsional response of the foundation in a layered half-space. The optimal model with frequency-independent parameters is subsequently utilized to analyze the dynamic amplification factor of the soil-foundation system. The results of this study indicate that the optimal model accurately captures the dynamic interactions occurring under torsional loading, with the dynamic amplification factor closely aligning with those obtained from a finite element program. The findings confirm the viability of the suggested method, showcasing its capability to effectively simulate soil-foundation interactions in torsional foundation vibration problems.