In this work, the bearing loads of a flywheel-based kinetic energy recovery system caused by gyroscopic torques and dynamic forces during vehicle maneuvering are investigated. This paper is a follow-up study to a preliminary investigation where the flywheel was assumed to be rigidly supported, thus neglecting the effect of rotor precession. At finite stiffnesses of real bearings, however, the flywheel is enabled to move, due to the compliance of the bearing itself, relative to the vehicle chassis with high angular velocities. Based on the equations for elastic rotor-platform interactions, which relate the vehicle’s roll, pitch and yaw rate with the internal transverse torques acting on the elastically supported flywheel, the radial bearing loads are re-investigated in this work for some selected standardized driving maneuvers. The simulation results of the present work are consistent with the results of the rigid model, provided that the elastic approach is subjected to high bearing stiffnesses. However, it is shown that for less rigid bearings the solutions are progressively different. Bearing stiffnesses that produce nutation frequencies of the rotor equal to the natural frequencies of the vehicle’s suspension yield to substantially higher gyroscopic torques. The present study provides an overview of the flywheel bearing loading characteristics caused by gyroscopic torques induced during vehicle maneuvering and by the acceleration of the flywheel’s mass, and includes a parametric study for a range of radial bearing stiffnesses.