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A soft tissue elasticity measurement technique based on Magnetic Resonance Elastography (MRE) is presented. In this technique, a tissue specimen is encased in a gelatine-agar block with known elasticity modulus. This block is slowly compressed using a MRI compatible device and displacements are measured using a phase contrast MRI technique. These displacements are processed using an iterative MRE model and the tissue elasticity modulus is obtained. Another uniaxial indentation method for soft tissue elasticity measurement developed in our lab is also presented. To demonstrate the performance of these two methods, a small specimen of adipose tissue obtained from breast reduction was tested by both methods and good agreement was achieved.