Magnetorheological elastomers (MRE) have been synthesized on the basis of a silicon compound and a mixture of carbonyl iron particles of sizes 3–5 and 40–80 μm. Their viscoelastic properties have been studied by dynamic shear oscillations of various amplitudes on a stress controlled rheometer. The magnetic response of the obtained materials has been examined in a magnetic field applied perpendicular to the shear plane. It has been shown that under applied magnetic field both the storage G′ and loss G″ moduli became strain‐dependent. The values of G′ and G″ decrease with strain, while their ratio (the loss factor), G″/G′, growths with strain. The higher magnetic field is the more pronounced the strain dependence is. At small strain (up to 1%) MRE demonstrate a giant (more than 10 times) increase of the moduli. Some features of hysteretic behavior of MRE under simultaneously applied magnetic field and external mechanical force have been elucidated. Temperature has a negligible effect on viscoelastic properties and stability of the developed MRE. A damper on the basis of MRE has been designed and its properties have been examined.