In this study, we present a theoretical framework for characterizing the performance of two-dimensional displacement and strain estimators. Specifically, we derived the Cramer-Rao lower bound for axial and lateral displacements estimated from radio frequency echo data. The derived analytical expressions include the effects of signal decorrelation, electronic noise, point spread function (PSF), and signal processing parameters (window size and overlap between the successive windows). We modeled the 2-D PSF of pulse-echo imaging system as a sinc-modulated spatial sine pulse in the axial direction and as a sinc function in the lateral direction. For validation, we compared the variance in displacements and strains, incurred when quasi-static elastography was performed using conventional linear array (CLA), plane wave (PW) and compounded plane wave (CPW) imaging techniques. We also extended the theory to assess the performance of vascular elastograms. The modified analytical expressions predicted that CLA and CPW should provide the worst and best elastographic performance, respectively, which was confirmed both in simulations and experimental studies. Additionally, our framework predicted that the peak performance should occur when 2 \% strain is applied, the same order of magnitude as observed in simulations (1 \%) and experiments (1 \% -- 2 \%).