Tire models used in vehicle dynamics simulation for CAE durability and ride comfort assessment need to be capable of predicting the non-linear deformation and enveloping characteristics which occur when traversing large road obstacles. Normally, transient dynamic characteristics of a rolling tire are determined from tire rig tests, and the tire parameters are transferred into multi-body system for vehicle dynamic analysis. However rig design limitations mean that tests cannot be carried out in the most severe conditions, particularly for traversing high ramp or large obstacles. However, using detailed FE tire models, such tests can be carried out virtually. A FE tire model was developed specifically for this purpose using explicit integration in ABAQUS™. Tire enveloping tests in traversing obstacles of different sizes were then carried out, virtually, using the validated FE tire model. Satisfactory results of transient responses were obtained by comparison with the experimental tests for the tire traversing obstacles with different heights. Tire transient dynamic behaviour was investigated by analysing the influence of tire rolling velocity and height of road obstacle on transient spindle responses, dynamic stiffness, together with tire deformation for the tire impacting obstacles. Finally, the investigation showed that longitudinal dynamic stiffness decreases when the tire traverses a higher obstacle. In addition, with the increase of height of road obstacle, the resonant amplitude of spindle force response as well as the tire deformation becomes larger in both longitudinal and vertical directions, especially for the tire rolling over 25 mm × 25 mm rectangular obstacle. Also, it is found that higher travelling velocity of the tire leads to higher resonant amplitude of spindle forces in the vertical direction.