Materials characterised by magnetorheological properties are non-classic engineering materials. A significant increase in the interest of scientific community in materials from this group can be observed over the recent several years. The results of research presented in this article are oriented on the examination of said materials’ mechanical properties. In order to do so, stress relaxation tests were conducted 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 examined samples increases along with the increase of magnetic field induction and decreases 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 has been indicated that the stress relaxation in the examined magnetorheological elastomer for the adopted time range (t = 3600 s) has a hyperbolic decline nature. The collected test results point to examined materials being characterised by extensive rheological properties, which leads to a conclusion that it is necessary to conduct further tests in this scope.