A numerical technique is developed for analyzing the coupled, transient, dynamic, interaction behavior of a high-speed, flexible vehicle propelled along a flexible guideway. The spatial behavior of the vehicle is modeled by the finite element method as an Euler beam with sectionally constant cross-section properties while a summation of the natural mode solutions are used to model the spatial behavior of the guideway. The magnitudes of the time-dependent front and rear vehicle suspension forces are assumed to be proportional to the relative displacements and displacement rates between the vehicle and the guideway at the points of support. The resulting time-dependent coupled differential equations of motion are then numercially integrated in time to obtain the transient dynamic response of the system. The results presented include a comparison of vehicle accelerations and guideway deflections, as predicted when the vehicle is rigid, to those obtained when the vehicle has various degrees of flexibility.