AbstractThis article documents the analytical study and feasibility of placing a tuned mass damper in the form of a limber rooftop moment frame atop relatively stiff structures to reduce seismic acceleration response. Six existing structures were analytically studied using a suite of time history and response spectra records. The analyses indicate that adding mass in conjunction with a limber frame results in an increase in the fundamental period of each structure. The fundamental period increase generally results in a decrease in seismic acceleration response for the same time history and response spectra records. Owing to the limber nature of the rooftop frames, non‐linear analysis methods were required to evaluate the stability of the rooftop tuned mass damper frame. The results indicate the addition of a rooftop tuned mass damper frame reduces the seismic acceleration response for most cases although acceleration response can increase if the rooftop frame is not tuned to accommodate the specific structure's dynamic behaviour and localized soil conditions. Appropriate design of the rooftop tuned mass damper frame can result in decreased seismic acceleration response. This translates to safer structures if used as a retrofit measure or a more economical design if used for new construction. Copyright © 2003 John Wiley & Sons, Ltd.