In this work, the instability damage modes of yield state of a steel tube at the tension side of a rectangular steel tube-confined concrete (RCFST) column under eccentric compression were classified into two types based on the coupling effect of slenderness ratio (λ) and eccentricity ratio (γ). The two types include the unilateral compression yield failure mode with a smaller value of γ and tensile and compressive yield failure modes on both column sides with a larger value of γ. Further, the parametric analyses were performed by employing the finite element (FE) method and the analytical analysis to test 16 groups of RCFST columns by varying the γ value with different λ values. It was observed that the results of the analysis for the mechanical properties like the responses of load-strain ( P-ε) and RCFST column instability modes correlated well with the results obtained in the experiments. Furthermore, the proposed theoretical method could be used to investigate the roles of γ as a controller against the instability in RCFST columns when compared with λ.