The running characteristics of a tire for a wheel are improved to provide a more quiet run, by attaching to an inner and/or outer surface of the tire vibration absorbing elements. Vibration absorbing elements may even be inserted into the tire material itself. The vibration absorbing elements are secured to the tire surface in a force and moment or torque transmitting manner by vulcanization or by a suitable adhesive. A strap may hold the individual absorbing elements together or the elements may form integral parts of the strap which is secured to the tire surface, for example, by a rubber vulcanizing operation. The vibration absorber elements may be secured to an inner tube instead of to the tire.