A new solution to geometrically nonlinear problems is presented. It has been found that the deflection curve equation expressed in terms of geometrical parameters for a compressed bar is a result of superposition by an Euler’s curve for two-force member in buckling equilibrium and a deformation equation for two-force member in stable equilibrium. Corresponding with the superposition of deflection curves, the load case of the compressed bar is divided into an axial force with a moment and an axial force with a shear force applied to the two-force member respectively. The analytic principle and the deflection curve equation for compressed bars can be applicable to geometrical nonlinear analysis or buckling problems, which is called analytical methods. The decision rule for the equilibrium property of the deflection curve expressions is presented. Practical applications of analytical methods show that some brief formulas can be obtained in the load case without shear forces.