The objective of this paper is to illustrate the application of a recently developed inelastic failure analysis method to frames under proportional cyclic loading. The method takes into account the effect of bending moment and axial force interaction in the formation of plastic hinges during the loading-unloading cycles. For structures where the axial forces are predominant, this interaction is important. The frame is loaded with a system of concentrated loads that are increased incrementally close to collapse and then unloaded. If, during the loading process, sections of the structure develop moments Mi and axial force Pi such that the points (Mi, Pi) are outside the yield curve, a redistribution takes place that brings these points onto the curve. After several load cycles, if the loading is not excessive, the structure adjusts to the loading and the response becomes stable (shakedown). In the process of redistribution, if other sections produce points outside the yield curve, the redistribution is repeated until no points (M, P) lie outside. As a first approximation, the moment-axial interaction (yield) curve was assumed to be a straight line. To improve the accuracy of the analysis, a nonlinear yield curve was derived that depends on the material properties of the section. Comparison of analytical results with those of other researchers indicate that the developed method can handle the issue of moment-axial interaction with accuracy.