An innovative device consisting of a flywheel equipped with a torsional vibration damper, based on the magnetorheological effect in elastomeric spring elements, is proposed in this paper. The feasibility study reports the dynamic behaviour of an automotive driveline equipped with the device aiming to explore the effectiveness of the damper in reducing the torsional oscillations of the flywheel, at low-speed regime, responsible for the vibro-acoustic phenomenon known as “gear rattle”. The spring elements of the device are constituted by magneto-rheological elastomeric samples, interposed between the flywheel and the damper disk, working for shear strains. Their dynamical characteristics can be properly tuned by varying the magnetic field surrounding the springs in order to mitigate the forced vibration causes of gear tooth impacts. The good attitude of the device in mitigating the rattle phenomenon is demonstrated by comparing the results provided by a numerical drive line model, equipped with a “monolithic” flywheel, with those obtained by adopting the present innovative vibration damper. The angular accelerations, resulting from the collisions between the teeth during the operation under “idle” conditions at different angular speeds, are thus compared.