Abstract This paper describes the behavior and design of a new self-centering frictional damper. This device is based on conic friction surfaces that lead to a flag-shaped hysteretic behavior. Its self-centering property and different possible configurations make it a very versatile device to be used in seismic applications of high-rise buildings subject to earthquakes. A simple mathematical model is presented first to describe the cyclic behavior of the device. Then, important variables related with the geometry and materials used in the device are analyzed to better understand their influence on the hysteretic behavior of the damper and optimize its design. Different friction materials, rubber samples, and coil springs are tested in the laboratory for the design of a proof-of-concept prototype. To test the theoretical model, the 115 kN large-scale damper was manufactured and dynamically tested in the laboratory obtaining excellent agreement between the theoretical and experimental results. Finally, a detailed finite element model was generated to study the local stress concentrations of the different components of the device as well as compare the hysteretic behavior for different possible configurations using metallic and rubber springs.