In this study, the performances of one-dimensional and two-dimensional least-squares strain estimators (LSQSE) are compared. Furthermore, the effects of kernel size are examined using simulated raw frequency data of a widely-adapted hard lesion/soft tissue model. The performances of both methods are assessed in terms of root-mean-squared errors (RMSE), elastographic signal-to-noise ratio (SNRe) and contrast-to-noise ratio (CNRe). RMSE analysis revealed that the 2D LSQSE yields better results for phased array data, especially for larger insonification angles. Using a 2D LSQSE enabled the processing of unfiltered displacement data, in particular for the lateral/horizontal strain components. The SNRe and CNRe analysis showed an improvement in precision and almost no loss in contrast using 2D LSQSE. However, the RMSE images for different kernel sizes revealed that the optimal 2D kernel size depends on the region-of-interest and showed that the LSQ kernel size should be limited to avoid loss in resolution.