Tissue elasticity assessment is is used in clinical applications from cancer diagnosis to prosthesis fitting. Elastography, using ultrasound to image tissue elasticity to replace digital palpation, includes methods which measure small volume tissue response to high-frequency acoustic excitation and bulk responses following quasi-static loading. Such techniques are well explored and used clinically; however, the goal of quantitative elasticity estimation remains unfulfilled. Additionally, tissue's elastic nonlinearity prevents either approach from providing elasticity information relevant to low-frequency loading as applied by a prosthesis on the lower-limb residuum during gait. This thesis presents research towards the development of a technique utilising the parametric array to exert an acoustic radiation force over small tissue areas under loading frequencies similar to those of gait. The resulting acoustic field magnitude is shown to depend on the elastic properties of the tissue it is developed within. An approach is presented which provides the foundations for a possible medical device to provide high resolution, low frequency, quantitative tissue elasticity information, to aid the prosthetist during fitting or offer the opportunity for automation.