Since the 1980s, there have been many research activities devoted to quantitatively characterizing and imaging human tissues based on sound speed, attenuation coefficient, density, nonlinear B/A parameter, etc., but those efforts have not yet reached the stage of commercialization. However, a new imaging technology termed elastography, which was proposed in the early 1980s, has recently been implemented in commercial clinical ultrasound scanners, and is now being used to diagnose prostates, breasts, thyroids, livers, blood vessels, etc., more quantitatively as a complementary adjunct modality to the conventional B-mode imaging. The purpose of this article is to introduce and review various elastographic algorithms for use in quasistatic or static compression type elasticity imaging modes. Most of the algorithms are based on the crosscorrelation or autocorrelation function methods, and the fundamental difference is that the time shift is estimated by changing the lag variable in the former, while it is directly obtained from the phase shift at a fixed lag in the latter.