We describe techniques for automatically acquiring observations of a deforming object and for estimating a model of the deformation from these observations. A robotic system was developed for measuring deformation, and has been previously reported (Pai et al., 2000, 2001). The present paper describes new techniques for the estimation of deformable models based on discrete Green's functions, from measurements acquired using stereo vision and a robot arm's position and force sensors. This kind of robotic measurement presents new challenges for measurement and estimation, that we address here. Our techniques for robotic acquisition of deformable, object models have potential applications in robotics, haptic interfaces, simulation, computer graphics and virtual reality.