The present paper proposes an original scheme for the dynamic analysis of the vehicle–bridge interaction (VBI) between trains and curved in-plan bridges. Key features are the three-dimensional vehicle dynamics formulation, and the matrix statement of the equations which condense the VBI dynamics, making the scheme generic. The analysis brings forward the interaction along the radial and torsional sense of curved bridges, which are often neglected for straight bridges. Specifically, the study shows that the (centrifugal and Coriolis) forces generated due to the curved path govern the lateral dynamics of the vehicle–bridge system when the curvature and/or the velocity are high.