Thin reinforced concrete cylindrical shells, commonly used in silos, storage tanks, and offshore platform legs, combine high strength-to-weight ratios with efficient load-bearing capacity. Their slender geometry, however, makes them highly susceptible to buckling, and existing studies on metallic or composite shells inadequately capture the behavior of concrete shells with embedded steel. This study presents a numerical investigation of thin reinforced concrete cylindrical columns under axial compression, focusing on the influence of reinforcement details and column geometry on critical buckling loads. Finite element simulations and parametric eigenvalue analyses were performed using Abaqus to identify buckling modes and evaluate stability. Results show that increasing the longitudinal bar diameter from 10 mm to 16 mm raised the first-mode buckling load from 9.420×10⁷ N to 9.524×10⁷ N, while increasing the number of bars from 8 to 12 increased the load from 9.394×10⁷ N to 9.463×10⁷ N. Column length had the most significant impact: extending from 750 mm to 1000 mm reduced the first-mode load from 9.463×10⁷ N to 6.195×10⁷ N. Eigenvalue analysis revealed classical global buckling modes, with the first mode governing instability. The findings indicate that larger reinforcement and higher bar quantity enhance buckling resistance, with diameter improving axial rigidity and bar number improving circumferential stiffness distribution. Nevertheless, geometric slenderness dominates structural stability, underscoring that reinforcement optimization alone cannot fully counteract buckling risk. These results provide critical guidance for designing thin concrete shells, highlighting the importance of simultaneous control of geometry and reinforcement detailing to prevent structural failure.