The dynamic mechanics model was built up to analyze the contact-impact between drill string and wellbore according to the characteristics of contact-impact, based on non-linear finite element method and Lagrange method. The dynamic mechanics equations were deduced by the dynamic mechanics model. The stress and deformation field of drill string with different parameters of bottom hole were obtained and tested by experiments and numerical simulation respectively. And also, the propagation laws of stress wave generated by contact-impact in drill pipe were studied. The comprehensive results indicate that the numerical results agree well with the actual dynamic process of contact-impact. The stress waves generated by contact-impact cause the change of stress. The contact-impact between drill string and wellbore under air drilling is the main reason for early drill string failure.