In recent decades, magnetorheological elastomer (MRE) has been widely used in engineering applications as vibration absorbers or isolators due to its field-dependent property. Thus, researches on the correlations of the variables and MRE behaviors are increasingly needed. This study aims to characterize and simulate magnetorheological behavior of elastomer filled with carbonyl iron and NdFeB particles under uniaxial tension, compression, and pure shear modes. First, tensile tests were performed for both isotropic and anisotropic magnetorheological elastomer (MRE) with carbonyl iron particle (CI), under the magnetic field of a pair of permanent magnets, to observe the feasibility of a portable, lightweight setup without the need of power supply. It turned out that the MR effect was apparent but not significant enough for real application. Also, there was a negative MR effect for anisotropic MRE when the magnetic flux is vertical to the particle chains. The compression test showed that Neodymium magnet powder (NdFeB) filled specimen always had higher compressive strength than the CI specimen. The outcome helped to the complementation of hard particle MRE characterization. A systematic shear test was conducted on isotropic CI and NdFeB MRE specimens. The shear test was divided into two parts. The first part observed the large-strain behavior of each specimen under a steady magnetic flux; 0, 200, 400, and 600 mT magnetic flux was applied during this part. NdFeB MRE specimens showed very little change in shear strength under different flux, while CI MRE was influenced substantially. The second part is conducted under dynamic flux ranging from -600 mT to 600 mT with small oscillation displacement. It turned out the hard MRE specimens had far more significant storage modulus than its counterpart. The result of the shear test proved that hard MRE has lower magnetization saturation and high storage modulus, and it is now further characterized. COMSOL simulation for tensile testing showed fair agreement with the experimental outcomes. Further improvements were proposed to make the model practical for future MRE studies.