Elasticity is an important physical property of biological tissues. Differences in elasticity can help facilitate the diagnosis of tumors and their extent. Magnetic Resonance Elastography (MRE) tries to visualize images of tissue elasticity by externally applying shear stress on the surface of an imaging object. Applied shear stress induces internal displacements that can be measured from MR phase images. In order to conduct MRE imaging experiments, we need to first develop a vibrator. We found that there does not exist enough technical information to design the MRE vibrator. In this paper, we describe the theory, design and construction of an MRE vibrator. We report the performance of the developed vibrator using two different test methods. We found that the vibrator successfully induces enough internal displacements that can be imaged using an MRI scanner. We suggest future studies of numerous MRE imaging experiments using the vibrator.