Abstract: For a more common situation, in order to estimate the in-plane second-order effect of the elastic members under compressing, there seems no convenient and accountable method other than the complicated direct analysis method is available. Based on the differential equation of the in-plane second-order effect of a constant-section column under a uniform axial compression, the orthogonality relation of its buckling modes is proved, and the stability of all possible equilibrium states is discussed. Furthermore, the in-plane second-order effect is adopted by buckling modal series method for the first time, and its accuracy is demonstrated by several typical situations. For the computational complexity and awful accuracy of some specific situation, a simplified method is proposed in which only the first order in-plane result and the axial force and the deform shape of its first buckling mode are required. And the efficiency and accuracy of this new method are evaluated by several typical situations.