Techniques have been described in the literature to enable multidimensional strain rate estimation. They are based on multidimensional velocity estimation. One of the problems in obtaining robust lateral strain rate estimates is the fact that lateral velocity estimates are intrinsically noisier than axial ones. The aim of this study was to find the optimal estimator for tracking of the radiofrequency patterns both in axial and lateral directions. Performances of the following estimators were investigated using simulations: cross-correlation, normalized cross-correlation, sum of absolute differences and sum of squared differences. Two-dimensional (2-D) velocity estimation was not feasible using cross-correlation. However, normalized cross-correlation, sum of absolute differences and sum of squared differences showed accurate axial and lateral results. For smaller window lengths, sum of squared differences was found to be the preferred estimator for 2-D velocity estimation using a 1-D kernel.