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To simplify the calculation of the maximum load at which instability occurs for reinforced-concrete pipe columns under eccentric compression, a method based on the transformed cross-sectional area of the column and the concrete secant modulus of elasticity is proposed, consisting of an iterative process in which a sequence of lateral deflections is at column mid-height. The method assumes the deflected shape of the column as a half cosine wave. Analytical results were compared with experimental values obtained from 16 reinforced-concrete pipe columns. Using deflection at column mid-height recorded during the loading process, a typical load-deflection curve can be plotted and used to describe column behavior. The experimental results demonstrate that the failure of concrete columns is a process. The starting point is the cracking load point, when cracks are initiated in the concrete of the tensile zone of the critical cross-section of specimens. The maximum load point is the top of the failure process, and then the maximum bending moment occurs. The first point represents instability while the second one corresponds to the strength failure of the columns. The experimental results are close to the analytical values. The method is simple and can be used for stability analysis of reinforced-concrete pipe columns.