A general numerical simulation method is presented for the analysis of the dynamic interaction problem between a large-span concrete culvert, discretized by a plane strain finite element model (FEM), and a dynamic system of vehicle traversing at various speeds. The vehicle is represented as a mass-spring-damper FEM system with seven degrees of freedom. The time-variable coupled dynamic system is solved by a step-by-step solution technique using Newmark’s integration scheme. The backfill soil elastic modulus is modeled as varying linearly with depth below the ground surface. Several numerical examples are investigated by modifying different parameters such as backfill height and road surface stiffness, respectively. The dynamic displacement response for the mid-span point of the concrete culverts is analyzed, as well as the displacement impact factor. The research results demonstrate that the impact factor changes with the vehicle speed and strongly depends on the road surface roughness conditions.