In this paper, an analysis of vehicle-bridge interaction problems, taking into account the dynamic effects induced by vehicle bouncing due to roadway surface irregularities and varying vehicle speeds, is presented. The problem formulation and solution methodology include the effects of vehicle suspension systems, the vehicle travelling path, and the arbitrary boundary conditions and geometry of the bridge superstructure. The kinematic coupling reflecting the dynamic interaction between the traversing vehicle and the vibrating bridge superstructure is explicitly treated in the problem. Vehicle models used in this study take into account the stiffness and damping characteristics of vehicle suspension and tires, and permit the inclusion of a variety of truck configurations. The spatial discretization of the governing differential equation of the vehicle-bridge system is based on the finite element method. The resulting matrix ordinary differential equation is then discretized with respect to time on the basis of the Newmark method. The process of reduction of a partial differential equation into a matrix ordinary differential equation through a spatial discretization procedure, and then solving this expression using a time integration technique, is referred to as the numerical method of lines. Since the consideration of the vehicle-bridge interaction introduces non-linearity into the problem formulation, a multi-predictor-corrector scheme is adopted in the solution procedure to obtain accurate results. Numerical examples, illustrating the influence of roadway surface irregularities and vehicle deceleration on the dynamic response of bridge structures, are provided to illustrate the validity and efficiency of the proposed formulation and solution methodology.