In this paper, we address the problem of simultaneously recovering the 3D shape and pose of a deformable and potentially elastic object from 2D motion. This is a highly ambiguous problem typically tackled by using low-rank shape and trajectory constraints. We show that formulating the problem in terms of a low-rank force space that induces the deformation, allows for a better physical interpretation of the resulting priors and a more accurate representation of the actual object's behavior. However, this comes at the price of, besides force and pose, having to estimate the elastic model of the object. For this, we use an Expectation Maximization strategy, where each of these parameters are successively learned within partial M-steps, while robustly dealing with missing observations. We thoroughly validate the approach on both mocap and real sequences, showing more accurate 3D reconstructions than state-of-the-art, and additionally providing an estimate of the full elastic model with no a priori information.