We are developing a method for imaging the elastic properties of tissue using unmodified clinical equipment and techniques that are similar to standard clinical exams. Our work with in vivo data from human subjects suggests that elasticity imaging provides new diagnostically significant information. For example, we can observe a nonlinear stressstrain relationship among tissues. Both the accuracy and variance of the displacement estimates must be understood to verify that observation. A significant body of work in algorithm development, computer simulation and phantom experiments precedes this effort. Much of that work addressed the variance in 1-D displacement estimates. The displacement estimate variance for a two-dimensional (2-D) search with a 2-D data kernel can be adequately studied using simulated echo data. The accuracy of displacement estimates when the true displacement is unknown, as with biological tissue experiments, is more difficult to mimic and is studied using data acquired from in vivo breast imaging. Methods to reduce displacement estimate variance and verify displacement estimate accuracy are presented.