The motivations of the application of shakedown analysis to the earthquake-resistant design of ductile moment-resisting steel structures are presented. The problems which must be solved with this application are also addressed. The illustrative results from a series of static and time history nonlinear analyses of one-bay three-story steel frame and the related discussions have shown that the incremental collapse may be the critical design criterion in case of earthquake loading. Based on the findings, it was concluded that the inelastic excursion mechanism for alternation load pattern, such as in earthquake, should be the sidesway mechanism of the whole structure for the efficient mobilization of the structural energy dissipating capacity and that the shakedown analysis technique can be used as a tool to ensure this mechanism.