Pathological phenomena often change the mechanical properties of the tissue. Therefore, estimation of tissue mechanical properties can be of clinical importance. Ultrasound elastography is a well-established strain estimation technique. Until recently, mainly 1D elastography algorithms have been developed. A few 2D algorithms have also been developed in the past. Both of these two types of technique ignore the tissue motion in the elevational direction, which could be a significant source of decorrelation in the RF data. In this thesis, a 3D elastography algorithm that estimates all the three components of tissue displacement is implemented and tested statistically. In this research, displacement fields of mechanical models are simulated. RF signals are then generated based on these displacement fields and used as the input of elastography algorithms. To evaluate the image quality of elastograms, absolute error, SNRe, CNRe and CNRasse are computed. The SNRe, CNRe and CNRasse values are investigated not only under different strain conditions, but also in different frame locations, which forms 3D strain filters. A statistical comparison between image qualities of the 3D technique and 2D technique is also provided. The results of this study show that the 3D elastography algorithm outperforms the 2D elastography algorithm in terms of image quality and robustness, especially under high strain conditions. This is because that the 3D algorithm estimates the elevational displacement, while the 2D technique only estimates the axial and lateral deformation. Since the elevational displacement could be an important source for the decorrelation in the RF data, the 3D technique is more effective and robust compared with the 2D technique.