We present a new approach for the analysis of the left ventricular shape and motion based on the development of a new class of volumetric deformable models. We estimate the deformation and complex motion of the left ventricle (LV) in terms of a few parameters that are functions and whose values vary locally across the LV. These parameters capture the radial and longitudinal contraction, the axial twisting, and the long-axis deformation. Using Lagrangian dynamics and finite-element theory, we convert these volumetric primitives into dynamic models that deform due to forces exerted by the datapoints. We present experiments where we used magnetic tagging (MRI-SPAMM) to acquire datapoints from the LV during systole. By applying our method to MRI-SPAMM datapoints, we were able to characterize the 3-D shape and motion of the LV both locally and globally, in a clinically useful way. In addition, based on the model parameters we were able to extract quantitative differences between normal and abnormal hearts and visualize them in a way that is useful to physicians.