Abstarct: Magnetorheological elastomers (MREs) are a kind of smart materials its mechanical properties especially rheological features can be adjusted by applying an external magnetic field. MREs are fabricated by embedding micron sized iron particles into a rubber like material matrix such as elastomer. These magnetizable particles can be distributed homogeneously (Isotropic MRE) or to be formed such a chain-like columnar structures (Anisotropic MRE) in a matrix. MREs have two unique characteristics such as variable stiffness and variable damping that can be used mostly in vibration control in different mechanical devices and also changing its natural frequencies. Therefore, in order to fabricate and utilize MRE in various applications, suitable advanced model capturing dynamic characteristics of MRE, is completely essential and important. The first step in modeling of dynamic behavior of MRE is identifying and interpreting the viscoelastic and mechanical properties of this materials in presence of various magnetic field as well as different loading conditions. In this study viscoelastic behavior of a MRE specimen by using of available experimental data from an oscillatory shear test is investigated and interpreted; then this behavior are represented by strain-stress hysteresis loops. In order to study dynamic behavior of MRE, a lot of strain-stress curves are plotted. These strain-stress hysteresis loops illustrating the viscoelastic nature of MRE, equivalent stiffness (the slope of main axis of strain-stress loops) and equivalent damping (area inside the hysteresis loops) that their shapes baxsed on the experimental data, indicating its dependency on the external magnetic field as well as loading conditions. In the dynamic oscillatory shear regime the shape of strain-stress loops are usually symmetric hysteresis. Additionally, the trend of shear storage modulus of MRE baxsed on the frequency from 0.1 Hz to 8 Hz is completely nonlinear indicating the strong dependency of shear storage modulus to the strain-rate. In order to predict the dynamic behavior of MRE a modified Kelvin-Voigt viscoelastic model is proposed. The proposed viscoelastic model describes relationships between shear stress and shear strain of MREs baxsed on input frequency, shear strain and magnetic flux density very accurately. Unlike the previous models of MREs, the coefficients of this model, calculated by nonlinear regression method in parallel with Genetic algorithm, are constant at various harmonic shear loads such as strain and strain-rate and only depend on the magnetic field. With these constant coefficients there is no need to implementing tough optimization algorithms at each new different loading condition of strain and strain-rate. Consequently, the stiffness and damping properties of MREs can be controlled just by adjusting the external magnetic field at each arbitrary loading conditions. Then, the proposed model in a control algorithms will work faster.