While reconstruction and tracking of rigid and articulated objects from video have been widely studied, modeling 3--D deformable surfaces remains a challenging problem, especially when using a single camera. The problem would be totally under-constrained without an appropriate deformation model, that is, one flexible enough to account for all possible configurations but controlled by sufficiently few parameters for effective optimization.Physics-based models have been extensively investigated as a potential answer to this problem. They have been shown to be excellent at fitting noisy image data and handling highly deformable objects. However, it is important to realize that many of these models rely on oversimplified, often quadratic, regularization terms to couple their degrees of freedom. These terms do not always accurately represent the physics of what is known as large deformations in the Mechanical Engineering community. This requires higher order terms to represent highly non-linear stresses and strains.In this project, we will develop models designed to work under more challenging conditions by accounting more accurately than current approaches for the material properties of surfaces, while striving to retain the simplicity of the original deformable models. This will increase the robustness of the algorithms that rely on such models, without significantly increasing their computational complexity.