Changes in tissue stiffness correlate with pathological phenomena that can aid the diagnosis of several diseases such as breast and prostate cancer. Ultrasound elastography measures the elastic properties of soft tissues using ultrasound signals. The standard way to estimate the displacement field from which researchers obtain the strain in elastography is the time-domain cross-correlation estimator (TDE). Optical flow (OF) methods have been also characterized and their use keeps increasing. We introduce in this paper the use of a Modified Demons Algorithm (MDA) to estimate the displacement field and we compare it with OF. A least-squares strain estimator (LSE) is applied to estimate the strain from the displacement. The input for the algorithm comes from the ultrasound scanner standard video output; therefore, its clinical implementation is immediate. To test the algorithm, a tissuemimicking phantom was modeled as a 10x10x5 cm region containing a centered 10mm cylindrical inclusion three times stiffer than the surrounding material, and its elastic behavior was simulated using COMSOL Multiphysics 3.2 software. Synthetic pre- and post-compression (1.25%) B-mode images were computer generated using FIELD 11 ultrasound simulator. Afterward, the algorithm was tested with a commercial CIRS breast elastography phantom, applying a 2% freehand compression. Axial displacement fields and strain figures are presented and in the case of the synthetic one compared to the around truth given by the FE software. Although other researchers have used registration methods for elastography, as far as we know, they have not been used as stand alone but together with elastic modulus reconstruction or FE which iteratively varies material properties to improve registration.