Abstract: According to the buckling behavior of compression members, this paper propose a mechanical model, which use the weakening to the midspan lateral stiffness of the compression member by axial force to characterize the axial force’s negative stiffness. By this model, the mechanical meaning of the effective length for non-sway frame was elaborated. Based on this model and the principle of equal equivalent negative stiffness, the equivalent relationship between the top load and the intermediate load acting on a frame column was established, and then the equivalent load factor formula was derived. Through this factor, an intermediate load can be converted to a top load, so that the stability of a frame can be checked by the effective length gained from Code, without recomputation. Then, the equivalent force method is proposed. This method can solve the stability problem of a non-sway frame under multiple-varying axial force easily with a good accuracy, thusly it can meet the requirements of engineering applications. The results show that the equivalent force method can be used for engineering design and theoretical calculations with good precision and accuracy,.