The TDS changed the drive mode and established a simple, flexible multi-body drill string system. The system consists of a derrick, a hoisting system, TDS, and a drill string system, and is inserted into a long, narrow borehole. The drill string then interacts with mud, the borehole wall, and the bottom hole, which generates resonance and increases the risk of drilling accidents. Natural frequency, which is related to the structure of the drill string, determines critical speed. In a vertical well, the transverse, torsional, and longitudinal fluid–structure interaction vibrations of the flexible multi-body drill string system within 1,700 m was analysed using the ANSYS. The natural frequency and the associated critical speed for different bottomhole assemblies (BHAs) were obtained. Results show that reasonably selecting the TDS rotation speed and optimizing BHA offer practical engineering applications for increasing drilling speed, reducing drilling accidents, and improving economic returns.