Damping is a critical phenomenon in determining the dynamic behavior of animated objects. For yarn-level cloth models, setting the correct damping behavior is particularly complicated, because common damping models in computer graphics do not account for the mixed Eulerian-Lagrangian discretization of efficient yarn-level models. In this paper, we show how to derive a damping model for yarn-level cloth from dissipation potentials. We develop specific formulations for the deformation modes present in yarn-level cloth, circumventing various numerical difficulties. We show that the proposed model enables independent control of the damping behavior of each deformation mode, unlike other previous models.