Mechanical properties of tissue have long been exploited by the physician to diagnose disease by palpation of masses. Generally, lesions are stiffer than their surrounding tissue, which exhibit different characteristic response to acoustic radiation force excitation from the surrounding tissue. The Acoustic Radiation Force Impulse (ARFI) imaging generates images of localized displacements in tissue by using radiation force induced from long pulses with hundreds of cycles. The localized micron-scale displacements are tracked by correlation-based methods. The displacement is then used to explicitly determine the spatial distribution of the mechanical properties of the tissue. Normalized cross correlation has the best performance of time-delay estimation in ultrasonic signals. However, the acquired RF echo data are required to be up-sampled to GHz so as to give micron scale precision between lags. Consequently data processing is computationally expensive and not suitable to real-time application. In this paper, two time-domain methods (Loupas and Phase Zero) and one frequency-domain (Cross Spectrum) method are compared using both simulated echo signals and phantom signals obtained through medical ultrasound system. The 2D phantom imaging is also provided.