This paper presents the characterization of damping behavior as characterized by hysteresis for farm equipment tires and time domain numerical simulation of off-road tire rolling using finite element techniques. The hysteretic behavior is characterized by the load-displacement curves from static nonrolling vertical loading tests. Using a highly simplified finite element model based solely on tire catalog information and general constructional information, a hysteresis material model is used to simulate the hysteretic load-displacement behavior of farm tires. By choosing appropriate parameters for the hysteresis model, the static nonrolling finite element analyses results correlate very well to the experimental results. The fitted hysteresis material model is then used to simulate the dynamic rolling of a tire dropping off a curb. The bouncing vertical acceleration is of great interest to off-road tires. First, implicit dynamics is used to simulate the rolling using the calibrated hysteresis model. Very good correlations between the simulation results and vehicle test results are obtained. For better off-road rolling performance, the hysteresis model is recalibrated to reduce the vertical acceleration of the tire after the first bounce following the drop-off. The hysteresis model is replicated in explicit dynamics using an Abaqus/Explicit VUMAT subroutine to simulate the dynamic tire rolling behavior. By introducing additional damping and creep dissipation, the vertical acceleration is attenuated in excess of 50% after the first bounce following the drop-off to improve riding comfort. This hysteresis characterization has been shown to give good agreement with test data on nonrolling tests and dynamic drop-off tests. All modeling and solutions were performed using commercially available Abaqus software.