Smart materials are increasingly used in the fields of robotics, biomedical, automotive and aerospace applications. Smart materials undergoing large deformations, such as magnetorheological elastomers, electroactive polymers etc. exhibit large deformation under the application of external loading. These materials can be used for applications like artificial muscle actuators , vibration absorbers and bio-inspired devices. Among these, magnetorheological elastomers have gained significant popularity in the last decade due to ease of manufacturing, their high sensitivity, long range of deformation and efficient remote actuation. However, thin structures made of these materials are prone to instabilities, reducing the device efficiency and range of operation. In this work, we present the mathematical modeling of magnetorheological elastomers. The mathematical model will be used to understand the effect of various loading conditions, Maxwell stress and onset of instabilities.