The problem about computer simulation of whirl vibrations of a drill bit is considered. The dynamic process is assumed to be in an incipient stage when the bit rolls on the borehole bottom without reaching the well wall. Mathematic models of the bit moving based on assumptions of frictional (rolling with sliding) and kinematic (pure rolling) contact between the bit and borehole bottom surfaces are elaborated. The influence of the drill string (DS) bending flexibility and the bit shape on the whirl process is discussed. The most typical whirl phenomena are grounded due to computer simulation.