Design analysis method developed in this study did not use a safety factor that can be used for the design of steel structures that are capable of supporting heavy working load with the weight as light as possible in order to obtain an effective and efficient structure in terms of technical and economic. In this research program, a method of cut-off strength is used as a basis of predicting the strength of a square hollow steel section affected by the interaction of concentrated-compressive load and bending moment. The method cut-off strength is illustrated in the form of two plastic and elastic curves of loaddeflection, where the value of load at an intersection of these curves is assumed to be the theoretical strength of the steel section with respect to the interaction of concentrated-compressive load and bending moment. The plastic curve is established according to a load-deflection equation that is developed through the analysis of energy equilibrium on the plastic failure mechanisms model of the steel section. Meanwhile, the elastic one is established according to another load-deflection curve that is developed through the analysis of non linear elastic concept of the steel structure. This analytical method is implemented by using computer software. In order to measure the accuracy of the design of this analytical model developed in this program, its predicted results are verified using actual strength data obtained from a number of tests on the square hollow steel sections subjected to the interaction of concentrated-compressive load and bending moment to failure. Verification results indicate that the ratio of the analytical-predicted data and experimental one is still scattered within tolerable limits of ± 20 %.