Cable-stayed bridges require a careful consideration of the lateral force exerted by the deck on the towers under strong earthquakes. This work explores the seismic response of cable-stayed bridges with yielding metallic dampers composed of triangular plates that connect the deck with the supports in the transverse direction. A design method based on an equivalent single-degree of freedom approximation is proposed. This is proved valid for conventional cable-stayed bridges with 200- and 400-m main spans, but not 600 m. The height of the plates is chosen to (1) achieve a yielding capacity that limits the maximum force transmitted from the deck to the towers, and to (2) control the hysteretic energy that the dampers dissipate by defining their design ductility. In order to select the optimal ductility and the damper configuration, a multi-objective response factor that accounts for the energy dissipation, peak damper displacement and low-cycle fatigue is introduced. The design method is applied to cable-stayed bridges with different spans and deck–support connections. The results show that the dissipation by plastic deformation in the dampers prevents significant damage in the towers of the short-to-medium-span bridges under the extreme seismic actions. However, the transverse response of the towers in the bridge with a 600-m main span is less sensitive to the dampers. Copyright © 2017 John Wiley & Sons, Ltd.