Abstract: Ignoring the influence of damping to the vibration of drill strings，the equivalent networks have been given out for a single drill pipe or more of the same drill pipe according to the one-dimensional torsional and longitudinal vibration equation of a drill string. In accordance with the series connection equivalent networks， considering the boundary conditions of the drill string system, the equivalent networks and mechanical equivalent impedance of torsional and longitudinal vibration were derived，and then the principles and methods for determining the mechanical resonance frequency of torsional and longitudinal vibration have been given by using the mechanical equivalent impedance. The resonant frequencies of two drill string systems were calculated by the equivalent network method and ANSYS finite element method. The calculation results indicate that using the equivalent network method to calculate the resonant frequency of torsional and longitudinal vibration of a drill string system is an effective method. It is easy to use and its calculating results are same with those calculated by the ANSYS finite element method.