Magnetic resonance elastography (MRE) is an important new method used to measure the elasticity or stiffness of tissues in vivo. While there are many possible applications of MRE, breast cancer detection and classification is currently the most common. Several groups have been developing methods based on MR and ultrasound (US). MR or US is used to estimate the displacements produced by either quasi-static compression or dynamic vibration of the tissue. An important advantage of MRE is the possibility of measuring displacements accurately in all three directions. The central problem in most versions of MRE is recovering elasticity information from the measured displacements. In previous work, we have presented simulation results in two and three dimensions that were promising. In this article, accurate reconstructions of elasticity images from 3D, steady-state experimental data are reported. These results are significant because they demonstrate that the process is truly three-dimensional even for relatively simple geometries and phantoms. Further, they show that the integration of displacement data acquisition and elastic property reconstruction has been successfully achieved in the experimental setting. This process involves acquiring volumetric MR phase images with prescribed phase offsets between the induced mechanical motion and the motion-encoding gradients, converting this information into a corresponding 3D displacement field and estimating the concomitant 3D elastic property distribution through model-based image reconstruction. Fully 3D displacement fields and resulting elasticity images are presented for single and multiple inclusion gel phantoms.