A numerical investigation is conducted to obtain the eigensolution of a deep-hole drilling shaft system. The rotating drilling shaft is modeled as a Rayleigh beam that conveys cutting fluid and is subjected to torque, compressive axial force, and support constraints. The governing equation of the drilling shaft system for lateral vibration is obtained by considering fluid-structure interaction, rotational inertia, gyroscopic effect, effect of motion constraints, and frictional damping generated by the surrounding fluid. The influence of cutting fluid flow velocity, rotational angular velocity, torque, compressive axial force, and support constraints on the natural frequency and stability of the drilling shaft system is examined. Cutting fluid flow velocity, compressive axial force, and torque decrease the natural frequency of the system, whereas rotational angular velocity and support constraints improve system stability.