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With the exploitation of oil and gas underground, the engineering has developed toward the direction of deep well, even super deep well, the problem of fatigue of drill string has a great effect to drilling engineering. Resonance is one of the main reasons that induces drill string fatigue. In this paper drill string of deep well is object being studied. The models about axial vibration, lateral vibration and torsional vibration are set up. Modal vibrations of drill string are studied. Rules of all sorts of nature frequency are obtained by drilling instance, and analysis about vector plot of nodes is obtained. This paper proves theory bases for optimizing drill tool of deep well and drilling parameter and reducing drill string failure.