This paper proposes an efficient method to capture and augment highly elastic objects from a single view. 3D shape recovery from a monocular video sequence is an underconstrained problem and many approaches have been proposed to enforce constraints and resolve the ambiguities. State-of-the art solutions enforce smoothness or geometric constraints, consider specific deformation properties such as inextensibility or ressort to shading constraints. However, few of them can handle properly large elastic deformations. We propose in this paper a real-time method which makes use of a me chanical model and is able to handle highly elastic objects. Our method is formulated as a energy minimization problem accounting for a non-linear elastic model constrained by external image points acquired from a monocular camera. This method prevents us from formulating restrictive assumptions and specific constraint terms in the minimization. The only parameter involved in the method is the Young's modulus where we show in experiments that a rough estimate of its value is sufficient to obtain a good reconstruction. Our method is compared to existing techniques with experiments conducted on computer-generated and real data that show the effectiveness of our approach. Experiments in the context of minimally invasive liver surgery are also provided.