As a novel technology, the mechanical stable platform can effectively improve the temperature resistance of the automatic vertical drilling system, but its working characteristics are still not yet clear. In this paper, theoretical mechanics is introduced to establish the critical deviation angle model, in order to evaluate the sensitivity of the mechanical stable platform to well deviation. Multi-body dynamics simulation is applied to mutually verify the models and further analyze the effect of vibration. The results show that the critical deviation angle is not only affected by the platform design parameters, but also by the system speed and external vibration. When the system angular velocity is less than the critical angular velocity ωc (3.76 rad/s), the critical deviation angle αC′ gradually decreases with the decreasing angular velocity until it approaches the extreme deviation angle αl (5.1°). The critical deviation angle is jointly affected by the amplitude A and frequency B of torsional vibration. When A>500°/s and B > 8 Hz, its variation range is between the αl (5.1°) and the critical deviation angle αc (7.03°). The critical deviation angle is jointly affected by the amplitude E and frequency F of axial vibration, with its value always greater than αc , but very small range of variation (0.2°). Torsional vibration plays a dominant role in torsional-axial coupled vibration, and the additional effect of axial vibration is relatively small. The results obtained herein are significant for further understanding and improvement of the performance of the mechanical vertical drilling system.