Smart materials are materials by which their properties are able to be altered due to external stimuli such as temperature, pressure and magnetic field. Magnetorheological Elastomer (MRE) is a type of smart composite material consisting of a polymer matrix embedded with ferromagnetic particles. In the presence of an external magnetic field, its mechanical properties such as stiffness change due to the interaction between the magnetic particles. It has been used in many applications such as vibration dampers and isolators. Unwanted vibration in machines can cause severe damage and machine breakdown. Vibration in rotary machines can cause severe damage and machine breakdown. Vibration isolation has been in interest of many researchers for many decades. In this work, semi-active vibration isolator using MRE is proposed for a potential used in drilling system in order to isolate the torsional vibration. This research focuses on studying MRE computationally and experimentally. Analytical simulation study was done by utilizing different MRE models from the literature on a base motion isolation (base excitation) system as a preliminary study in order to understand the characteristics of MRE. Results showed that as the magnetic field increases, the stiffness of MRE increases by a shifting in the natural frequency of the system from the transmissibility curve, so that vibration is reduced. In addition, a numerical modeling of MRE using COMSOL Multiphysics software was done to study the effect of the magnetic field on its stiffness in axial and torsional modes. The MRE consisted of a cylindrical silicon rubber embedded with 12 iron particles. An increase of 28.75% and 20.12% of the stiffness was obtained in axial and torsional modes, respectively. The transmissibility analysis revealed that as the magnetic field increases, the linear and torsional stiffness increases as well which cause a shifting in the transmissibility curves to the right indicating that the natural frequency of the system is increased. Furthermore, MRE was fabricated with a 35% volume fraction (VF) consisted of a silicon rubber and iron particles. MRE was used in torsional vibration isolation on the proposed drilling system. It was fitted with a coupler and attached on the shaft (drill string) in order to study its efficiency in vibration isolation under a magnetic field. Two tests were conducted on the drilling application used in this research, the first test was a hammer impact test by which the system was excited by an input and the response was obtained. The torsional transfer function (TTF) analysis showed that the natural frequency of the system has shifted from 13.9 Hz to 17.5 Hz by the influence of the magnetic field around the MRE. Finally in this work, another test was done during the continuous rotation of the drilling prototype; results showed that the amplitude of rotation is attenuated by the presence of the magnetic field.