The paper develops the analytical expression of the moment-curvature relationships (n-m-φ relationships) of concrete encased steel section under constant axial compression. In the analysis, the stress-strain relationship of concrete is assumed to be parabolic up to maximum stress and after that to have a linear falling branch, and that of steel is assumed to be elastic-perfectly plastic. Concrete encased section is divided into two components ; plain concrete section and H-shaped steel section. In both sections, the stress distribution is classified into four fundamental cases. When material properties and dimensions of a section are given, the n-m-φ relationships of the components can be expressed by analytical form as a function of curvature and neutral axis ratio. For the case of the concrete encased steel section, the pattern of stress distribution are classified into 12 fundamental cases under the combination of two components. Carrying moment of each component at arbitrary stage of loading can be easily calculated using curvature and neutral axis ratio, since neutral axis ratio is obtained from equilibrium in axial force. Carrying moment of concrete encased steel section can be obtained by summation of those components, analytically. Accuracy of the proposed analytical method was confirmed by numerical method. The proposed method can be directly applicable to member analysis.