On diesel vehicles, we frequently experience the phenomenon that low frequency fore and aft vibration of a vehicle, occurs at acceleration, does not decline in amplitude easily and rather increases finally. The phenomenon has recently attracted great concern in driveability problems on diesel vehicles. This phenomenon can not be explained well by the simple torsional vibration model of the powertrain with one node, which has been used so far successfully to analyze low frequency fore and aft vibration of a vehicle. So, we have assumed that the undamped vibration occurs through the interaction of the engine and the powertrain. Taking this interaction into consideration, we have constructed a simulation model, with which the undamped vibration can be simulated accurately. By this simulation model, we have estimated the order of magnitude of the effects of various design parameters affecting the undamped vibration. Particularly, it has been found that the characteristics of injection pump governor, significantly affect the undamped vibration.