This study presents comprehensive analytical and numerical modeling of the force interactions in friction pairs, specifically between the “clamping beam – friction wedge" and “friction wedge – friction rod," using the freight car model 18-9597 as a representative case. By integrating both analytical derivations and finite element simulations, the research identifies rational design parameters that ensure stable, efficient, and long-term performance of the spring-friction damping unit in freight car bogies. The study not only enhances the understanding of contact mechanics and frictional behavior under dynamic loading but also provides practical insights into the geometric optimization of friction elements. The derived formulas for coupling reactions as functions of friction pair geometry offer a valuable tool for engineers in designing more reliable systems. The findings are applicable to both the modernization of existing railway rolling stock and the design of new-generation freight wagons, potentially contributing to improved safety, durability, and maintenance efficiency across the rail industry.