Abstract: Based on the interaction model of bit and formation, the force caused by rock and bit is defined as the bottom boundary condition of drilling string. Under some simplified condition and by means of elastic bar theory and unit method, the axial vibration model according to interaction between bit and formation
and elastic deformation of drill string is established during drilling process. Based on the boundary condition and initial condition, the axial model is soluted by difference methods. It is a theoritical foundation for further understanding of the dynamic behavior and kinetics rule of drilling string and rock bit,modifying design method, controlling well track and preventing
failure early.

Key words: Bit, String Vibration, Model, Calculation Method, Computerized Emulation