Cancer is known to induce significant structural changes to tissue. In most cancers, including breast cancer, such changes yield tissue stiffening. As such, imaging tissue stiffness can be used effectively for cancer diagnosis. One such imaging technique, ultrasound elastography, has emerged with the aim of providing a low-cost imaging modality for effective breast cancer diagnosis. In quasi-static breast ultrasound elastography, the breast is stimulated by ultrasound probe, leading to tissue deformation. The tissue displacement data can be estimated using a pair of acquired ultrasound radiofrequency (RF) data pertaining to pre- and post-deformation states. The data can then be used within a mathematical framework to construct an image of the tissue stiffness distribution. Ultrasound RF data is known to include significant noise which lead to corruption of estimated displacement fields, especially the lateral displacements. In this study, we propose a tissue mechanics-based method aiming at improving the quality of estimated displacement data. We applied the method to RF data acquired from a tissue-mimicking phantom. The results indicated that the method is effective in improving the quality of the displacement data.