Estimation of tissue stiffness is an important means of noninvasive cancer detection. Existing elasticity reconstruction methods usually depend on a dense displacement field (inferred from ultrasound or MR images) and known external forces. Many imaging modalities, however, cannot provide details within an organ and therefore cannot provide such a displacement field. Furthermore, force exertion and measurement can be difficult for some internal organs, making boundary forces another missing parameter. We propose a general method for estimating elasticity and boundary forces automatically using an iterative optimization framework, given the desired (target) output surface. During the optimization, the input model is deformed by the simulator, and an objective function based on the distance between the deformed surface and the target surface is minimized numerically. The optimization framework does not depend on a particular simulation method and is therefore suitable for different physical models. We show a positive correlation between clinical prostate cancer stage (a clinical measure of severity) and the recovered elasticity of the organ. Since the surface correspondence is established, our method also provides a nonrigid image registration, where the quality of the deformation fields is guaranteed, as they are computed using a physics-based simulation.