The current research and development of 2D (matrix-shaped) transducer arrays to acquire 3D ultrasound data sets provides new insights into medical ultrasound applications and in particular into elastography. Until very recently, tissue strain estimation techniques commonly used in elastography were mainly 1D or 2D methods. In this paper, a 3D technique estimating biological soft tissue deformation under load from ultrasound radiofrequency volume acquisitions is introduced. This method locally computes axial strains, while considering lateral and elevational motions. Optimal deformation parameters are estimated as those maximizing a similarity criterion, defined as the normalized correlation coefficient, between an initial region and its deformed version, when the latter is compensated for according to these parameters. The performance of our algorithm was assessed with numerical data reproducing the configuration of breast cancer, as well as a physical phantom mimicking a pressure ulcer. Simulation results show that the estimated strain fields are very close to the theoretical values, perfectly discriminating between the harder lesion and the surrounding medium. Experimental strain images of the physical phantom demonstrated the different structures of the medium, even though they are not all detectable on the ultrasound scans. Finally, both simulated and experimental results demonstrate the ability of our algorithm to provide good-quality elastograms, even in the conditions of significant out-of-plane motion.