The quantitative estimation of regional cardiac deformation from 3D image sequences has important clinical implications for the assessment of viability in the heart wall. Such estimates have so far been obtained almost exclusively from Magnetic Resonance (MR) images, specifically MR tagging. In this paper we describe a methodology for estimating cardiac deformations from 3D echocardiography (3DE). The images are segmented interactively and then initial correspondence is established using a shape-tracking approach. A dense motion field is then estimated using a transversely isotropic linear elastic model, which accounts for the fiber directions in the left ventricle. The dense motion field is in turn used to calculate the deformation of the heart wall in terms of strain in cardiac specific directions. The strains obtained using this approach in open-chest dogs before and after coronary occlusion, show good agreement with previously published results in the literature. They also exhibit a high correlation with strains produced in the same animals using implanted sonomicrometers. This proposed method provides quantitative regional 3D estimates of heart deformation from ultrasound images.