The individual soft tissues in the human body, such as liver, prostate, thyroid and breast, can each be characterized by a set of mechanical properties. Among these properties, the stiffness, or Young’s modulus, is of particular interest, as disease processes or abnormal growths introduce changes in the tissue stiffness. For example, cirrhosis is associated with an increase in stiffness in the affected region(s) of the liver, and the severity has a strong positive correlation with the measured liver tissue stiffness. Although the conventional ultrasound image is produced by changes in acoustic properties, most notably acoustic impedance (equal to density times sound speed), it is in fact possible to measure tissue strain ultrasonically, by performing ultrasound imaging while the tissue region of interest is mechanically perturbed. Although in principle incorrect, such strain imaging methods are commonly referred to as ultrasound elastography imaging. While tissue strain can reveal the presence of stiffness changes, its diagnostic value is limited due to the inability to reveal the magnitude of the stiffness change. Still, strain imaging is a feature on several commercial scanners. There does in fact exist an elegant, but complex and quite expensive, quantitative ultrasound method of imaging the elasticity of soft tissues, called Supersonic Shear imaging (SSI). However, a much lower cost method of quantitatively imaging tissue elasticity would be useful, especially if the method can be implemented with only minor modifications to existing ultrasound scanner design. This dissertation research deals with an attempt of designing and testing such a method. Ultrasound elastography encompasses a number of diverse techniques, roughly categorized by the mechanical perturbation method into two main groups: quasi-static and dynamic methods. Dynamic elastography requires a vibrating source, either separate or integrated with a transducer, making the imaging system cumbersome, especially for the portable systems. Quasi-static elastography only requires conventional ultrasound hardware, however current techniques remain qualitative with unknown stress distribution. This dissertation focuses on the investigation of free hand quantitative quasi-static elastography, aiming to real time assessment. Our proposed low cost real-time ultrasound elastography system is based on determining an axial strain and an axial stress over a region of interest, i.e., an axial strain image and an axial stress image are required. By taking the axial stress/axial strain ratio for each pixel in the image, an actual elasticity image is established. To achieve this goal, our system needs to ultrasonically measure the mechanical strain fast and accurately over a specified image plane; likewise, the system needs to be able to calculate the mechanical stress over the same image plane in real time. Now, the stress imaging will require us to apply a quasi-static force function and also to be able to quantify this force function. There are two major research efforts we have made to implement a low cost real-time ultrasound elastography system. The first important topic of this dissertation involves the development of a novel displacement and strain estimator based on analytical phase tracking (APT), which has been demonstrated to give better performance in terms of accuracy, resolution and computational efficiency (approximately 40 times faster than the standard time domain cross correlation method). The second important topic is the stress field reconstruction, with efforts in: 1) integrate force sensors into a single linear array transducer probe, with the goal of quantifying the applied force function; 2) propose a superposition method based on Love’s analytical equation to calculate the stress distribution, where this solution is computationally fast enough to allow real time stress field estimation; 3) analyze the accuracy of the proposed stress method using finite element analysis as a reference on different simulated phantoms. The final objective is to combine the strain and stress information together for quantitative elastography. Correspondingly, we have implemented experiments to evaluate the method on homogeneous and inhomogeneous phantoms of various types. Results show that this method is able to distinguish medium with different stiffness. We have conducted experiments to study the feasibility and improve the accuracy of this estimation technique based on phantoms with known elasticity. In principle, such a technique could be used to image the distribution of Young’s modulus under quasi-static compression, with specific applications to medical imaging.