Abstract: Materials characterized by magnetorheological properties are non-classic engineering materials. A significant increase in the interest of the scientific community about this group of materials could be observed over the recent years. The results of research presented in this article are oriented on the examination of the said materials’ mechanical properties. Stress relaxation tests were carried out on cylindrical samples of magnetorheological elastomers loaded with compressive stress, for various values of magnetic induction (B1 = 0 mT, B2 = 32 mT, B3 = 48 mT, and B4 = 64 mT) and temperature (T1 = 25 °C, T2 = 30 °C, and T3 = 40 °C). The results of these tests indicate that the stiffness of the examined samples increased along with the increase of magnetic field induction, and decreased along with the increase of temperature. On this basis, it has been determined that: the biggest stress amplitude change, caused by the influence of magnetic field, was σ0ΔB = 12.7%, and the biggest stress amplitude change, caused by the influence of temperature, was σ0ΔT = 11.3%. As a result of applying a mathematical model, it was indicated that the stress relaxation in the examined magnetorheological elastomer, for the adopted time range (t = 3600 s), had a hyperbolic decline nature. The collected test results point to the examined materials being characterized by extensive rheological properties, which leads to the conclusion that it is necessary to conduct further tests in this area.