The computation of skin forces and deformations for tactile rendering requires an accurate model of the extremely nonlinear behavior of the skin. In this work, we investigate the characterization of finger mechanics with the goal of designing accurate nonlinear models for tactile rendering. First, we describe a measurement setup that enables the acquisition of contact force and contact area in the context of controlled finger indentation experiments. Second, we describe an optimization procedure that estimates the parameters of strain-limiting deformation models that match best the acquired data. We show that the acquisition setup allows the measurement of force and area information with high repeatability, and the estimation method reaches nonlinear models that match the measured data with high accuracy.