We present a new method for analyzing the 3D motion of the heart's left ventricle (LV) from tagged magnetic resonance imaging (MRI) data. Our technique is based on the development of a new class of volumetric physics-based deformable models whose parameters are functions and can capture the local shape variation of an object. These parameters require no complex post-processing in order to be used by a physician. These volumetric models allow the accurate estimation of the shape and motion of the inner and outer walls of the LV as well as within the walls. We also present a new technique for calculating forces exerted by tagged MRI data to material points of the deformable model. Furthermore, by plotting the variations over time of the extracted LV model parameters from normal heart data we are able to quantitatively analyze and compare the epicardial and endocardial motion.