The behavior of slender reinforced concrete columns, (S.R.C.C.), under short-term eccentric axial loads has attracted the attention of numerous researchers. Several methods of stability analysis of slender columns have been reported, but they appeared complexity for use. In this research, a simple numerical method with rapid procedures and little calculations is deduced to provide more accurate results of the buckling load, or, the failure load, (F.L.), of S.R.C.C. under uniaxial bending. The method is applicable to material failure and buckling failure due to consideration of both material and geometric non-linearity in the analysis. The F.L. is calculated by the proposed method for previously experimented columns and compared with that obtained by the other numerical methods. The comparison is extended to include results of the F.L. of the same columns using the approaches of some international codes for R.C. structures. The F.L. of slender columns is predicted by the proposed method for different affecting factors of the column stability, as well as for normal and high compressive strengths of concrete. The results of F.L. obtained using the proposed method appear good agreement and more convergence to the experimental results.