In order to quantify the material damping of deformed flexible fibers, a linear viscoelastic sphere-chain model based on the discrete element method is presented. In the model the interaction between any two neighboring spheres connected by a visual bond is modeled as springs and dash-pots which can be characterized by the bond stiffness and bond damping coefficient, respectively. Then the model is applied to simulate the bending of cantilever beam under static load and the motion of fiber in the simple shear flow, respectively, and the predictions agree well with those of classic analytic solutions, available experimental data and previous simulation results. Regarding to the damping behavior of deformed flexible fibers, the results suggest that the damping coefficient of an individual fiber mainly depends on the aspect ratio of the fiber and the viscous bond damping coefficient. A correlation is formulated to quantify the relationship between the damping coefficient of the local bond and that of the flexible fiber. Generally, to enhance the global damping of fibers with extremely large aspect ratio, the bond rolling friction torque is more effective than the viscous bond damping. Those findings will be meaningful for the development of numerical modeling of flexible fibers. (C) 2015 Elsevier B.V. All rights reserved.