In this paper,the method of establishing the torsional vibration model of drilling string and rock bit and the process of simulation analysis are introduced.The interaction between bit and rock and elastic deformation of drilling string in the process of petroleum drilling which caused the torsional vibration of the drilling string and rock bit is main considered in establishing the model.The torsional model is solved by difference method.Based on the models,the simulation analysis software of drilling string and rock bit is designed,and simulation calculation and analysis of the tortional vibration of drilling string and rock bit under different conditions are computed,and the dynamic behavior and kinetics regularity of drilling string and rock bit in drilling are obtained.