Quantitative description of the cardiac left ventricle (LV) motion is desirable to assist in detecting myocardial motion abnormalities. It has been recognized that the torsion component of the LV movement is considerably more difficult to track than its radial counterpart. We develop a motion estimation method that estimates three-dimensional (3-D) LV motion vector field (MVF) that includes the twisting motion from four-dimensional (4-D) gated myocardial perfusion (MP) emission computed tomography (ECT) images. The method is implemented through searching for an MVF that minimizes a cost function consisting of the image matching error between two frames and the weighted strain energy constraint that prevents physically implausible movement. The strain energy is calculated on segmented heart voxels with physical parameters that model the material properties of the myocardium. The close-to-optimal weight of the strain energy was obtained by minimizing the root-mean-square errors of the estimated MVF from standard NCAT phantom images simulating gated MP data. The performance of this method has been quantitatively evaluated, in estimating MVF from NCAT generated images with specified motion corresponding to varied LV twisting angles (different from the standard phantom) and to regional LV motion defects. The estimated defect MVF can be distinguished from the estimated normal MVF.