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Ultrasound (US) elastography is an image processing technique used to evaluate the mechanical properties of soft biological tissue, making it a promising non invasive diagnostic and screening tool. The accessibility to the RF data of 2D transducers has led to a focus on 1D and 2D techniques. However, the inherent 3D movement of tissue under loading forces during image acquisition inevitably produces out-of-plane motion; a significant source of noise in 2D elastograms. This paper presents a direct 3D axial strain estimation algorithm which exploits fundamental image processing techniques to form a method which is both robust and computationally efficient. Displacement estimation is first carried out using integral images/volumes that allow for a quick and near exhaustive motion tracking scheme with maximum window overlap. Subsequently, paired regions are subjected to a fast spectral shift measurement for axial strain estimation that utilizes Fourier cross correlation to reduce the computational burden previously associated with spectral methods. The resulting system was found to be more robust to displacement estimation noise than standard gradient based techniques while remaining significantly faster than adaptive local registration methods. The 3D method was tested on simulated and real US data obtained from freehand scanning.