The stress–strain relationship of concrete is different under different boundary conditions, load paths, and environments. Identification of the stress–strain relationship of concrete for different structures and design conditions is critical to the engineering design of structures. Because direct measurement of local stress is impossible without interrupting the original local stress–strain condition, various indirect methods have been developed to derive stress–strain relationships of concrete. An analytical method for deriving the stress–strain relationship of concrete from eccentrically loaded column tests is extensively studied in this paper, through rigorous mathematical derivation and rational analytical studies. Detailed and rigorous equations and computational procedures for columns with an arbitrary shape of cross section are obtained. Instability of the calculated stress–strain curve or large scattering of results, a critical problem of the analytical method, is resolved through proper selection of equations and computational procedures. Application of the method reveals the real shape of the stress–strain relationship of fiber–reinforced polymer (FRP)-confined concrete under eccentric loading for the first time.