In many diseases such as cancer, atherosclerosis, and hepatitis, dramatic changes in the mechanical properties of the soft tissue are observed. Elastography is a technique for imaging tissue stiffness and may be used to detect disease and evaluate its degree of progression. Demand for elastography is perceived due to growing number of individuals dealing with cancer, late detection and financial and emotional cost of biopsy. Several methods have been proposed for elastography over the past two decades which are different in the excitation method or the measured quantity. These techniques can be divided into two general groups: shear wave imaging and strain imaging. This project aims to prepare the appropriate background for developing technical knowledge of new ultrasound elastography techniques such as shear wave imaging methods. By comparing ultrasound elastography techniques, the most proper method is selected for precise analysis. Elastography simulation is performed for elastic and viscoelastic models in three steps: excitation, wave generation, and elasticity map reconstruction. Elasticity reconstruction is performed using time-to-pick displacement method and Radon sum transformation method. Simulation goal is to validate shear and Young's modulus reconstruction methods. To compare accuracy, precision, and resolution of the simulation output with experiment, gelatin phantoms with desired stiffness are developed and their Young's moduli are measured through elastography and compression test. It is observed that shear modulus and elasticity map reconstruction is possible with proper resolution, accuracy, and precision. Experiments and simulations complement each other and simulation is representative of the part of the experiment which is done inside the elastography system processor. Keywords: Ultrasound elastography, Soft tissue, Mechanical property, Tissue stiffness, Shear wave, Shear modulus, FEM simulation, Phantom