Using a finite element model, this paper investigates the torsional vibration of a drill string under combined deterministic excitation and random excitation. The random excitation is caused by the random friction coefficients between the drill bit and the bottom of the hole and assumed as white noise. Simulation shows that the responses under random excitation become random too, and the probabilistic distribution of the responses at each discretized time instant is obtained. The two points, entering and leaving the stick stage, are examined with special attention. The results indicate that the two points become random under random excitation, and the distributions are not normal even when the excitation is assumed as Gaussian white noise.