In the field of small diameter deep hole coring drilling， in addition to the traditional lifting and coring methods， drilling methods such as wireline coring technology and screw motor bottom hole power tools are also widely used. Different bottom hole assembly （BHA） and drill strings together form flexible rods with a large slenderness ratio， which generate complex vibrations during the drilling process， profoundly affecting the safety of drilling engineering. At present， many mature analysis methods have been developed for the theory of pipe string vibration represented by drilling engineering， but research on the torsional vibration characteristics of pipe strings is still insufficient for the vertical hole structure of small diameter deep hole drilling， diamond bit grinding of rock layers， and especially when selecting different BHA and drilling methods. The finite element analysis method is suitable for solving problems with complex boundary conditions， and has good results in analyzing the vibration characteristics of drilling strings. Based on ANSYS software， a variety of typical BHA suitable for small diameter deep hole drilling are selected， and corresponding finite element analysis models are established to solve the relationship between factors such as hole depth， weight on bit， and the torsional vibration characteristics of the pipe string. A solution method for the critical rotational speed that may cause the joint vibration of the pipe string under different hole depths is given. This study can provide some reference for small diameter deep hole coring drilling engineering in terms of BHA selection， rotational speed selection， and string safety evaluation.