We propose a beamforming scheme for ultrasound imaging leading to the generation of two sets of images, one with oscillations only in the axial direction and one with oscillations only in the lateral direction. Applied to tissue elasticity imaging, this leads to the development of a specific displacement estimation technique that is capable of accurate estimation of two components of the displacement. The mean standard deviation for the axial displacement estimates is 0.0219 times the wavelength of the axial oscillations , and for the lateral estimates, it is equal to 0.0164 times the wavelength of the lateral oscillations . The method is presented and its feasibility is clearly established by a simulation work.