We present a new approach for the analysis of the left ventricular shape and motion that is 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 the 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 (MIR-SPAMM) to acquire datapoints from the LV during systole. By applying our method to MRI_SPAMM datapoints, we were able to characterize both locally and globally the 3D shape and motion of the LV 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.