Mechanical systems with rotary machines or rotating elements experience torsional vibration, which may lead to an extreme damage and wear. Conventionally, to isolate these undesirable structural vibrations, passive elastomer or torsional dampers are used. However, these passive vibration isolators are not adaptive to varying oscillation frequencies in real time. Due to the need for a real time adaptability and controllable stiffness, the research and development of a smart material called magnetorheological elastomer (MRE) is of interest. This paper presents the mathematical modelling and development of MRE with its implication in torsional vibration control. Based on the model and through experimental studies, the properties of the MRE such as stiffness and transmissibility factor in regard to varying magnetic fields are investigated. The change in magnetic field is achieved by changing the amount of applied current. It is found out that the stiffness of MRE increases with increasing magnetic field and consequently modifies system's natural frequency. This allows shift in the transmissibility curve to achieve minimum transmissibility factor in the applications involving varying frequency.