It seems likely that humans build internal models of objects that they explore haptically, and that the complexity of an internal model is not necessarily associated with complex exploratory procedures or the existence of visual input. Can a robot build a model of an object it touches or presses, and if so, can that model be used to render the object through a haptic interface? Or even simpler, can a robot estimate parameter values for a model already provided using data produced only by haptic exploration? This paper addresses the problem of parameter identification of hybrid dynamical systems, a class which contains systems of objects which make and break contact with one another. We propose the use of a hybrid sensitivity model as a basis for the construction of parameter identification algorithms. We distinguish between two components of a hybrid sensitivity model: sensitivity of states and sensitivity of switching instants to parameter variation, and we present two algorithms, one essentially based on each type of sensitivity. Simulation results demonstrating each algorithm are also presented.