Gun drills are widely utilized for deep hole machining due to their high aspect ratio, low stability, and susceptibility to vibrations, which can adversely affect machining accuracy and efficiency. During the machining process, cutting fluid must be injected through the drill rod to facilitate chip removal, resulting in a cross-sectional design with circumferential asymmetry. This asymmetry introduces more complex dynamic characteristics compared to conventional circular cross-section rotors. This study develops a Rayleigh rotor model of the gun drill rod and employs the Galerkin method to evaluate its free vibration characteristics and stability. The findings reveal that the gun drill rod exhibits distinct unstable speed ranges compared to circular cross-section rotors. Furthermore, the impact of various dimensional factors on the free vibration characteristics and stability of gun drill pipes was explored through detailed examination. The theoretical results were validated through comparative analysis with ANSYS simulations, confirming the reliability of the findings in this study.