In this paper, a 2-D locally regularized strain estimation method for imaging deformation of soft biological tissues from radio-frequency (RF) ultrasound (US) data is introduced. Contrary to most 2-D techniques that model the compression-induced local displacement as a 2-D shift, our algorithm also considers a local scaling factor in the axial direction. This direction-dependent model of tissue motion and deformation is induced by the highly anisotropic resolution of RF US images. Optimal parameters are computed through the constrained maximization of a similarity criterion defined as the normalized correlation coefficient. Its value at the solution is then used as an indicator of estimation reliability, the probability of correct estimation increasing with the correlation value. In case of correlation loss, the estimation integrates an additional constraint, imposing local continuity within displacement and strain fields. Using local scaling factors and regularization increase the method's robustness with regard to decorrelation noise, resulting in a wider range of precise measurements. Results on simulated US data from a mechanically homogeneous medium subjected to successive uniaxial loadings demonstrate that our method is theoretically able to accurately estimate strains up to 17%. Experimental strain images of phantom and cut specimens of bovine liver clearly show the harder inclusions.