Rotary drilling with roller cone bit is often accompanied by wide fluctuations of the weight on bit (WOB). In certain cases, the WOE periodically reduces to null. It has been postulated that in these cases the drill bit lifts off form the formation surface. The present study models the interaction among the lift-off of the drill bit, the WOE variation, and the modulation of the amplitude of the lobes on the formation surface. The analytical model is used to obtain numerical results for a specific drillstring. From these results it is inferred that the rotary speeds corresponding to the axial resonant frequencies of the system, determined from the functions of the driving point mobility and impedance at the drill bit, are critical regarding the wide fluctuations of the WOB; they may be associated with the sustenance of the lobes with large amplitude.