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Strain imaging has been performed using 1D, 2D and 3D ultrasound data. Usually, strain is only estimated in the beam direction, because of the availability of phase information. However, strain estimates in other directions are also desired, since most tissues are anisotropic. Beam steering enables measurement of different projections of the 2D displacement field while using phase information. The full 2D displacement field and strain tensor can be derived using multiple projections. This study aims at deriving the full 2D strain tensor by estimating only displacement along the beam while steering the beam at three angles, i.e. 0?, a positive, and a negative beam steering angle. Displacements were iteratively estimated using 2D cross-correlations. The 0? acquisition yielded the vertical displacement vector. Projection of the other measured displacements yielded the horizontal (lateral) vector. The full 2D strain tensor was derived using 1D least squares strain estimators. Since horizontal displacements and strains are usually the least accurate, these were first focused on. Horizontal displacements were estimated for simulated radiofrequency (rf) data of a block with a four times stiffer cylindrical inclusion before and after application of 2% vertical compression. Root mean squared error (RMSE) of the horizontal displacements were calculated for every symmetric pair of beam steering angles in the range of -30 to 30? with angular increments of 5?. The RMSE analysis was performed for signal-to-noise (SNR) levels of 5, 10, 20 and 50 dB. Beam steering combinations of about -25? and 25? were found to be most optimal. The technique's performance was maintained regardless of the SNR level. For an SNR of 5 dB a reduction in RMSE of up to 70% was observed. In analogy with the simulations, experiments were performed with a similar inclusion phantom made of polyvinyl alcohol. Using data from beam steering angles of -25?, 0? and 25? strain images were constructed for all stra- - in components and compared to strain images constructed without beam steering. The horizontal and shear strain images improved clearly with beam steering. Finally, the technique was also applied to derive radial and circumferential strain images for a homogeneous vessel phantom made of gelatin. Radially, SNRe and CNRe increased with 2.2 dB and 8 dB and circumferentially with 2.6 dB and 9.2 dB compared to non steered strain estimates. To conclude, the full 2D strain tensor can be accurately measured by using three beam steering angles.