This paper analyzes several important issues on the drill string system dynamics model and its numerical algorithm. Firstly, it introduces the commonly used numerical methods and contact algorithms, and analyzes the advantages and disadvantages of each method in detail. Secondly, it analyzes the application of explicit and implicit methods for the current stress iteration algorithm, and specifies the implicit algorithm should be used in the research of drill string system dynamics. This paper focuses on the research of damping model and bit-rock interaction model, solves the damping effect based on the theory of ocean wave mechanics, and establishes a simplified bit-rock interaction model. Finally, a virtual numerical simulation example shows that the method used in this paper can analyze the dynamic of drill string used in the 1,000-meter complex well bore. The research result of this paper has certain guiding meanings on the analysis of working behavior of extra-long pipe string in the complex well bore by using numerical methods in the oil field.