Accurately predicting deck accelerations in railway bridges subjected to high-speed trains is crucial for ensuring track quality, ballast stability, and the structural integrity of bridges. This requires a numerical model of the track-structure-subsoil system that strike a balance accuracy with computational efficiency. Existing literature reflects this trade-off. Some studies prioritize efficiency through simplified representa- tions of the foundation, subsoil, track, or bridge structure, while others emphasize accuracy by adopting highly detailed models of these subsystems. A fully detailed dynamic analysis of the coupled train, track, bridge structure, and subsoil system requires significant computing power. This explains why there are so few comprehensive models reported in the literature. Consequently, most existing algorithms address the vehicle-track-structure interaction problem without explicitly accounting for subsoil effects. These approaches usually rely on either direct methods to solve a globally coupled system of equations [1] or iterative methods to treat the subsystems separately [2]. Direct approaches provide an accurate representation of the coupling between the train and the track. However, they require the factorization of global, time-dependent system matrices at each time step, resulting in high computational costs. Iterative approaches reduce this burden by repeatedly solving the individual subsystems until convergence is achieved at the wheel-rail contact interface. Although these methods are computationally more efficient, they may suffer from convergence and stability issues. This study presents a novel algorithm that combines the strengths of both direct and iterative approaches. Building upon the localized Lagrange multiplier framework of [3], the method is expanded using an efficient representation of soil-structure interaction. An application example is presented to investigate the dynamic interaction among train, track, bridge structure, and subsoil. Particular emphasis is placed on soil-structure interaction effects, highlighting the contributions of subsoil stiffness and damping to the overall dynamic response.