This paper aims at constructing a stochastic model for the hysteretic behaviour of the nonlinear bit-rock interaction of a drill string under torsional vibrations using field data. The proposed model takes into account the fluctuations of the stick-slip oscillations and the hysteretic effect due to the nonlinear bit-rock interaction observed during the drilling process. These fluctuations are modelled by introducing a stochastic process associated with the variations of the bit-rock interaction during the drilling. The parameters of the stochastic model are calibrated with field data. Finally, independent trajectories of the proposed stochastic model are generated and used to simulate the stochastic response of the drill string torsional dynamics in presence of random bit-rock interaction. The stochastic model is then used to estimate statistics on the stability of the drill string.