The effect of cumulative damage on the strength requirements of degrading structures is assessed through the evaluation of the target ductility and corresponding strength reduction factors of simple degrading structures. While the reduction on ductility is established through the use of Park and Ang index, the suggestions given by Bojórquez and Rivera are used to model the degradation of the structural properties of the simple systems. Target ductilities and their corresponding reduced strength reduction factors are established for five sets of ground motions; most of them are recorded in California. The results given in this paper provide insight into all relevant parameters that should be considered during seismic design of earthquake-resistant structures. Finally, some recommendations to evaluate the effect of cumulative damage on seismic design are suggested.