In this paper, we propose a novel method to simultaneously track the deformation of soft objects and estimate their elasticity parameters. The tracking of the deformable object is performed by combining the visual information captured by a RGB-D sensor with interactive Finite Element Method simulations of the object. The visual information is more particularly used to distort the simulated object. In parallel, the elasticity parameter estimation minimizes the error between the tracked object and a simulated object deformed by the forces that are measured using a force sensor. Once the elasticity parameters are estimated, our tracking algorithm can be used to estimate the deformation forces applied to an object without the use of a force sensor. We validated our method on several soft objects with different shape complexities. Our evaluations show the ability of our method to estimate the elasticity parameters as well as its use to estimate the forces applied to a deformable object without any force sensor. These results open novel perspectives to better track and control deformable objects during robotic manipulations.