Rigidity of upper and lower limbs in Parkinson's disease (PD) is typically assessed via a clinical rating scale that is subject to human perception biases. Methodologies to quantify changes in rigidity associated with the angular position (stiffness) or velocity (viscous damping) are needed to enhance our understanding of PD pathophysiology and objectively assess therapies. In this proof of concept study, we developed a robotic system and a model-based approach to estimate viscous damping and stiffness of the elbow. Our methodology enables the subject to freely rotate the elbow using an admittance controller while torque perturbations tailored to identify the arm dynamics are delivered. The viscosity and stiffness are calculated based on the experimental data using least-squares estimation. We validated our technique using computer simulations and experiments with a nonhuman animal model of PD in the presence and absence of deep brain stimulation therapy. Our data show that stiffness and viscosity measurements can better differentiate rigidity changes than scores previously used for research, including the work and impulse scores, and the modified unified Parkinson's disease rating scale. Our estimation method is suitable for quantifying the effect of therapies on viscous damping and stiffness and studying the pathophysiological mechanisms underlying rigidity in PD.