Elastography is a relatively new technique in ultrasound or magnetic resonance imaging (MRI). This fact has motivated many investigators to investigate the preparation of tissue-mimicking material and the imaging of the tissue-mimicking phantom. In this article, an efficient numerical optimization method based on Quasi-Newton algorithm is presented for calculating a 2D strain image of tissue-mimicking material (TMM) sample. The first step in the proposed method is that the initial values for the displacement fields are estimated using the crosscorrelation method. Then, the numerical optimization method based on the Quasi-Newton algorithm is adopted to improve the displacement and strain through selecting one moving subfield. The basic idea of the proposed method is to construct an object function based on a homogeneous affine transformation between pre- and post-compression data and optimize the displacement and strain image for the initial displacement data. For a validation, the results of the proposed method compare with those of other numerical optimization methods. The simulated and experimental results demonstrate the potential of our two-step strategy for the strain imaging of tissue-mimicking phantom with high efficiency and accuracy. (C) 2015 Society of Plastics Engineers